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From the systems theory point of view the attempting was made to establish the most suitable logical and semantical conceptual definition for systems notions while maintaining the maximal compatibility in the theoretical field, which enable to bring together systems with any scale and complexity to...
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System research and information technologies| _version_ | 1866302306283159552 |
|---|---|
| author | Kolyada, Vladimir P. |
| author_facet | Kolyada, Vladimir P. |
| author_sort | Kolyada, Vladimir P. |
| baseUrl_str | http://journal.iasa.kpi.ua/oai |
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| datestamp_date | 2019-12-13T15:15:18Z |
| description | From the systems theory point of view the attempting was made to establish the most suitable logical and semantical conceptual definition for systems notions while maintaining the maximal compatibility in the theoretical field, which enable to bring together systems with any scale and complexity to a single strategy of interpretation of their dynamics. The special semantic clarifications for notions which generating theoretical ground were established. Thus specified fundamental and system-forming processes. Direct relations of specific terms and subtleties of differences of system notions, their roles for creating solid theoretical representation were highlighted. Some examples of the biochemical types are given. An explicit, semantic clarification of some concepts describing the dynamics of systems and states is proposed. |
| doi_str_mv | 10.20535/SRIT.2308-8893.2019.3.04 |
| first_indexed | 2025-07-17T10:24:29Z |
| format | Article |
| fulltext |
Vladimir P. Kolyada, 2019
Системні дослідження та інформаційні технології, 2019, № 3 41
UDC 530.1.007:575+577
DOI: 10.20535/SRIT.2308-8893.2019.3.04
TO THE THEORY OF SYSTEMS:
A BRIEF LOOK AT THE UNDERLYING OF NOTIONS
IN THE FIELD OF CONCEPTUAL CONTENT
VLADIMIR P. KOLYADA
Abstract. From the systems theory point of view the attempting was made to estab-
lish the most suitable logical and semantical conceptual definition for systems no-
tions while maintaining the maximal compatibility in the theoretical field, which en-
able to bring together systems with any scale and complexity to a single strategy of
interpretation of their dynamics. The special semantic clarifications for notions
which generating theoretical ground were established. Thus specified fundamental
and system-forming processes. Direct relations of specific terms and subtleties of
differences of system notions, their roles for creating solid theoretical representation
were highlighted. Some examples of the biochemical types are given. An explicit,
semantic clarification of some concepts describing the dynamics of systems and
states is proposed.
Keywords: theory of systems, notions, universal, evolution.
INTRODUCTION
Understanding system-forming phenomena represents itself a highly important
field of study, which allows to establish true mechanisms of genesis, develop-
ment, functional regularity and self-organization of world-perceived systems on
the fundamental level, particularly non-linear dynamic systems. Systems ap-
proach suggests not just mathematical modeling of some approximately isomor-
phic systems (whose dynamics are compatible or almost compatible with a certain
differential equation) but primarily comprehensive determination and interpreta-
tion systems notions that composing itself the essence of explanations for regular-
ity in the theory of systems. Based on exhaustive logical and semantical conclu-
sions in regard to notional definition that composing the units of metalinguistic
concept for current issue, we will attempt to specify possible discrepancies in in-
terpretation of systems dynamic from the point of view of system-based phenom-
ena wherein deviating from specific models (restrictions) or establishing compati-
bility of corresponded logic with as much as possible described systems, at least
in hypothetical field. A prerequisite is made for implementation of a general strat-
egy for defining a system without ignoring specialization i.e. avoiding particular
mathematical models on the one hand and statistical analysis methods, which is
not allowing to fully implement the quality compatibility of the systems under
consideration, on the other.
SUBSTRATUM (ENVIRONMENT)
The basis on which a function can be implemented can be considered as an envi-
ronment. Independently of how the level of abstraction the realization was caused,
Vladimir P. Kolyada
ISSN 1681–6048 System Research & Information Technologies, 2019, № 3 42
the material movement (according to the existing interpretation of modern sci-
ence) eventually happening as the initiator of the function. For the convenient rea-
son the set of all spaces can be named a real environment, defining as a universal
U and described as follows:
The real environment in system understanding primarily corresponds with
the conceptual definition of the active environment that in the inhomogeneous
space of which, relatively (†), stationary states exist (sustainable active environ-
ments on a spatial scale) the dynamics of which are caused by special, local in
relation to such systems, constraints (impulses, disturbances, or vice versa, ady-
namic iterations). The real substratum or environment has three major spaces –
material (physical) M, functional P and also informational I, when the material
substrate is identified to the state of the system, which behaves in accordance with
the natural (physical, chemical, etc.) constraints of environment when
,I+P+MU nnm
n
,IPM nnm
n
nnnm
n
m
n
IPPƒMM :)(: provided
,m,IP,M,n )( where n — dimension of action space, m — coefficient of
restrictions. In accordance with the systems approach and continuity problems,
the physical space can be formally identified with the functional space, when the
concepts of movement and action in a logical-semantic sense describe the same
observable phenomenon on some continuum set.
The functional environment (functional space) corresponds to an abstract
ideally isomorphic projection of the material substrate and expressed in the degree
of negentropy or its functional ordering. Informational environment (information
or signs space), is an abstract ideally isomorphic projection of the functional and
the material substrate accordingly and expressed in the degree of negentropy or its
informational order. Thus, is highlighting a separate class of functional and in-
formation systems that exist at a certain abstract level and are a consequence of
entropy-negentropy (chaos†) or a form (structure) of material substratum being at
the same time absolutely isomorphic to the material substrate. The environment is
a set of systems ideally isomorphic to each other, simultaneously acting in quali-
tatively different spaces when the unity of the environment is expressing through
the isomorphism. Therefore, in the process of analyzing a certain system, often,
the entire axis of related systems can be analyzed simultaneously.
An important characteristic of the functional environment is the tendency to
change its functional concentration from state to state (in the process of move-
ment) or analyzing from the perspective of the information environment —
a change in the information order. In other words, a functional substrate is more
functional than it is more ordered and more addicted to implement informational
order or information synthesis. It should be noted that the orderliness and stability
of the environment are not identical notions – orderliness tends to predetermine
sustainability, in turn, stability tends to negative orderliness.
The unity or atomicity of the real environment is caused not only by its in-
ternal isomorphic nature but also by the presence of cyclical conditioning of its
material, functional and informational components whose existence is possible
only in their equal dependence on each other. For example, in the absence of a
functional or informational component, the substrate would be in the first case a
model with no dynamics, changes, movement, and therefore progressive exis-
To the theory of systems: a brief look at the underlying of notions in the field …
Системні дослідження та інформаційні технології, 2019, № 3 43
tence. In the second case, the absence of communication possibilities between the
states generating the signal. This absence inevitably leads to a constant increase of
the entropy limit on any scale of the system and, to the progressive existence of
a real substrate accordingly.
As the environment moves and the functional concentration fluctuates, the
phenomenon of sustainability is formed inevitably and obviously predetermining
fundamental evolutionary movement whose dynamics have multiple progressive
polymorphism. It is also obvious that there is a phenomenon that predetermining
different behavior of the local environment while maintaining a general self-
similarity of action to some scale when system dynamics are described by local
characteristics ignoring the set of lower order using summation and upper order
using instantiation respectively. Such a pattern in the environment naturally indi-
cates the occurrence of attenuation of the dependence between actions in the
space of functions, when the index of functional importance decreases as the ac-
tion vector moves away from a function to a certain target state with minimal im-
portance. The scopes of such an “egocentric” set in the space of functions that
highlights the transition area of the function to the external environment and los-
ing its quality importance, defines the concept of the visibility limit for a certain
functional system.
The visibility limit of the system corresponds to the length of the vector or
scale of the system that the functional particular properties of which beyond its
boundaries no longer matter. From the point of view of the physical environment,
the visibility limit actually corresponds to the spatial geometric structure of the
system (which has fairly clear functional ambits).
RESTRICTIONS
It is important to note that the limitations that synthesize the deterministic prob-
abilistic characteristics of the system also constitute the essence of any state and
action. States and actions are the executive tools in the space of the environment
or phenomena that form the dynamics while restrictions are a direct determinant
factor. At the same time, all phenomena synthesized by environmental restrictions
certainly are cross-cutting and therefore interact at different levels with different
recursiveness and synthesized (including itself) probabilistic factors. We empha-
size that the concept of restriction means a non-classical increase in the “rigidity”
of the system’s dynamics due to the transformation or replacing the functions of
local sets and accordingly devoid the degree of freedom of a limited system. The
consequence of the conditional absolute removal of restrictions from a certain
system, obviously will be the primitivization of the system’s structure by devoid it
of the corresponding fundamental properties which predetermine the dynamics of
such a system in the environment. Formally, we can say that the restriction r cor-
responds to the function (attribute) of the set n of some system S in the material
environment, when Snf=r )( .
NOISE AND CHAOS
The concept of noise and chaos in a semantic sense have common features with
the only difference that noise is apparently a special case of chaos and closely
Vladimir P. Kolyada
ISSN 1681–6048 System Research & Information Technologies, 2019, № 3 44
related to the concept of dispersion, that is, a phenomenon that has a certain
source or beginning the gradual concentration of which differs as it moves, if spa-
tial restrictions contribute to this. The presence of noise in some state naturally
implies the existence of a source of such noise and thereby defining the element
of noise as part of the gradual dispersion as it moves, in the distal direction, func-
tional and information uncertainty increases (Lyapunov exponent). It can be con-
sidered that in relation to another system such an element of noise contains less of
functional importance. To achieve a scale of uncertainty that goes beyond the vis-
ibility (when turbulent flows form signs of homogeneity beyond the scale) the set
of such dissipation can correspond to the criterion of chaos†.
Thus, the only source of increasing uncertainty and negative ordering in the
real environment is the phenomenon of noise (or intersection of vectors nV of the
functional state A of the set a in the state B of the set b, when
,a=AV
n
=k
kaa
1
,b=BV
n
=k
kbb
1
ba VV ,
at n in continuity) coming from some state, that is the system or state is a
source of noise the dispersion dynamics of which generates a functional “pattern”
constituting the topological essence of the system. This is not directly about the
scenarios of the chaos appearance eg Ruelle–Takens, Pomeau–Manneville or Fei-
genbaum as noise generators, but about the structure of the dynamics in the
physical environment, where each state is an element of noise regardless of
whether such a state moves (on a certain scale) with a chaotic potential or not. An
example of an elementary formal representation of the appearance of homoge-
neity (an increasing uncertainty) is any n2 -dimensional model on the Poincaré
map with increasing energy (eg Henon–Heiles model) [1]. It is worth to noting
that isomorphic interpretations of such a phenomenon are undoubtedly relevant in
the functional and information spaces of any level of the hierarchy and probably
play a key role in understanding the origin of instability initiation.
The more distally the vector (action) of such a “pattern” is from its central
structure, the more its properties tend to be interpreted as the notion of the ran-
domness phenomenon (or increasing complexity as going beyond visibility) and
the less likely it is to form under pressure of restrictions. Obviously, with the re-
moval sources of noise step-by-step from the environment, primarily localized
“strange” (chaotic) attractors, it is possible to achieve complete determination of
any system. It seems that the reduction of restrictions increases the tendency to
acquire geometric invariance or self-similarity and fractal similarity of the real
environment in scale.
Entropy-negentropy, mainly and probably the only way, comes from inside
the state as functional and informational signals having a destructive or, on the
contrary, stable potential and further, as the scale increases, generates other state
models thus forming the essence of the system topology in the substrate.
The noisiness of the environment, as a result of restrictions, creates a prob-
abilistic† situation in the environment that forms an effective or progressive func-
tional substrate. The probabilistic situation in a logical-semantic sense is probably
identical to the quantitative measure (density) of the environment on a scale. The
probability of state synthesis is determined which somehow or another enters into
a dependent relation to the presence of a certain (e.g. high or low) probability
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Системні дослідження та інформаційні технології, 2019, № 3 45
of synthesis of another set which may also be included in other probabilistic de-
pendencies, etc. Thus, the hierarchical synthesis of states and their dynamics in a
probabilistic field, which in turn is a derivative of noise in a substrate, is self-
regulated.
There is an important feature of radiation in any state that can be observed,
when the noise pattern spreads the worse, the more the importance and specificity
of the system in which this pattern diffuses. Due to the fact that any state has an
atomic form, (when all vectors that nested in it are strictly determined by restric-
tions) the concept of state radiation is an abstract interpretation in the sense that
there is no empty space for any other vector to enter, due to their continuity or
infinite density. The notion of the absence of empty space in the state is inter-
preted as an estimation in a quasi-space that describing the possibility of replacing
one set by another if it were possible. In this case, it is impossible to replace the
noise distribution vector in a certain target state.
Dynamics in quasi-space during vector nV assimilation can form situations
(properties of restrictions) when the formations n+n VV 1 are not possible due to
congestion of the functional space at the same time, entry into the state is possible
only after free up a certain functional place in the state. It should be noted that the
concept of congestion is compatible only in the case of higher abstractions or ab-
stractions that have more than one functional space for their implementation, un-
like a functional environment that has one implementation space (material envi-
ronment) when the importance and its properties are defined. Biochemical
example of a similar phenomenon in general can be the mechanisms of proteins
repressors regulation [2, 3].
SYSTEM AND STATE
Previously, the following conceptual formulation of the system and state should
be clarified: the single iteration is a state, the system is at least one state, the sys-
tem forms at least one state.
Any system S is a determination of some emerging state by means of in-
coming action vectors )()( SSVS n and, as a result of this determination, the
possibility of influencing or regulating the final state or the vector itself leading to
such a state )()( nVSSS . Individual cases of such mechanisms are clearly rep-
resented for example in protein machines, in the regulation of gene expression
and lie in the ability to regulate such expression differentially, selectively control-
ling the expression of the type of a particular gene or protein and its amount [4].
In supercomplex systems, such regulation is already expressed in the pre-psychic
and mental apparatus of the regulation of behavior (movement).
Effective functional movement is a higher order shift of the environmental
functional structure relatively to the material set, with such a degree of preserva-
tion of this functional structure that will also preserve its informational row, at
least, in the visibility limit of the systems related to it, while the primary (lower
level) structure of the environment is certainly not capable to moving without
moving its isomorphic material structure. An example of a functional structure
shift, basically, without qualitative preservation of the information signal on the
scale, is the shift of the reading position by one or two nucleotides in the molecu-
Vladimir P. Kolyada
ISSN 1681–6048 System Research & Information Technologies, 2019, № 3 46
lar gene apparatus that is the transition to the second and third functional space. In
this case, it is possible both the preservation and the loss of functional transla-
tional consequences.
A similar effect occurs during the shift in higher functional fusion processes
when two or more functional structures that are shifted into each other assimilat-
ing into one unitary structure (it can be considered that such a union occurs when
after a merging the final function subsequently generates a signal identical to the
function signals, as if they had not merged). Classical isomorphic phenomena in a
probabilistic field can correspond to the formations of points or intersections of
trajectories in the phase space at the cross-section of an invariant tori set for Ham-
iltonian systems.
It is necessary to define the concept of the importance of the state. The state
importance degree of a set also has a rather abstract concept and in fact, it repre-
sents the entropy properties of a state in combination with the functional and in-
formational sets that are the components of such a state or determining it also
forming ordering and, as a result, stability. In turn, a state with a sufficient num-
ber of destructive signals is likely to be tend to the progression of negative order-
ing and negative importance accordingly. A suitable example of importance in a
biochemical scale substrate is highly conserved receptor domains with a high de-
gree of autonomy, for example, steroid or other hormones or proteins, collectively
characterized by a high degree of homology, both at the level of the material sub-
strate, when the amino acid sequence is the same or different and does not affect
functionally, and at the level of the functional information environment when se-
quences perform a single function (for example a DNA binding sites) [5]. On the
contrary, amino acid receptor sequences with a low degree of homology may have
low conservative, highly specialized, highly dependent, material and functional
information indicators, respectively. On the contrary, amino acid receptor se-
quences with a low degree of homology may have low conservative, highly spe-
cialized, highly dependent, material (amino acid sequence varies) and functional-
information (carry out various or closely related functions, or the functional abil-
ity is insignificant on the scale) indicators, respectively. It is important to empha-
size that at the same time similar properties are preserved even within different
taxonomic categories, which may indicate constellation genesis in duplicating
such a material and/or functional (with isomorphic topology and different mate-
rial structure in the functional case) structure raised under the restrictions of a
similar strategy (algorithm), or indicate congenitality for a specific ancestral gene,
due to the fact that quite often closely related proteins performing similar func-
tions have a common genetic ancestor or at least these genes were more or less
homologous.
Importance in the information substrate can also be interpreted as a measure
of the functional state stability. An example of informational destruction in a bio-
logical substrate can be the final death of the immune system B-cell with unsuc-
cessful V-D-J genes functional recombination forming the H- and L- antigen
chains [6] which is in the role of the functional essence of the cell without the
possibility of restructuring its purpose with no changing the scale, when entering
into another information vector at the current scale is impossible and therefore the
cell is phagocytosed through certain mechanisms dissolving in the environment.
Thus, the system is fragmented to a certain steady state where an attempt will be
made to reach the target state in fragments in accordance with the established
To the theory of systems: a brief look at the underlying of notions in the field …
Системні дослідження та інформаційні технології, 2019, № 3 47
restrictions. Such of destruction can be a particular example of the fluence phe-
nomenon and finiteness of importance.
From the informational point of view, the degree of the functional structure
importance predetermines, apparently, the saturation of signal or saturation can
probably be called as the amount of importance, that is, the number of vectors and
especially important vectors included in the signal and thus determining the de-
gree of importance of such a signal.
It should be noted specialization and variable properties of importance. Pre-
viously, we shall to determine an evolutionary peak notion, which is based on the
synthetic theory of evolution and synergetic, can be a system that is stable on long
evolutionary periods of time and corresponds to the maximum-specific categori-
zation of matter. For example, in life, this corresponds to the categories of the
species and subspecies.
A distinctive feature of systems that are more susceptible to the evolutionary
peak from less susceptible systems is the specialized feature of the direction of the
signals of such states or their inclusion in certain significant systems specific for
such a state (cycles, constellations, regulation, etc.). In this case, for example in
multicellular organisms, many unstable cells that have undergone degeneration
that destabilize the microprograms and accordingly the higher programs in which
they belong. The special and, on the contrary, universal functions of such a set
depend on variable factors that determine the importance of individual, func-
tional-information programs that run such cells. There are special factors that
have many dependencies, which in turn have their own algorithms for regulating
the importance and when changing their dynamics (self-destruction) they are ca-
pable of much more disturbing the main program, in contrast to a large number of
factors with insignificant importance, which is natural. In relation to the self-
destruction, it should be clarified that states with high importance (orderliness)
tend to be stable but also, the occurrence of a destructive signal that capable of
destabilizing and destroying such a state is permissible.
There is an important pattern in the environment - function-dependent states,
as a rule, tend to convergence† or reduce the distance of signal communications
as effectively as possible and of course the intensity of such a phenomenon is the
higher, the closer a state is localized to a certain evolutionary peak. Due to such a
convergence, only and only the function of the highest order )(xf of the formed
system P corresponds to the informational purpose I of the same order
,xfI ))(( because the final function is the limit functional-information structure
PIG of a certain scale of the set PIGU and can be performed only on such a
specific scale:
,GGGf=xfG IPPn+PI :)()( 1 ,xfGT +nPI 1)( k
n
=k
xfT )(
1
,
where T is some important set for .PIG
Separately, the functions )(xf of the set )(xf are characterized by a spe-
cific dependence that highly prepossessed to functional incompleteness and vul-
nerability with functional deviations from the usual scale or a measure of secon-
dary functional isomorphism in an environment where secondarity is expressed as
quantitative qualities without including the main informational purpose (the quin-
Vladimir P. Kolyada
ISSN 1681–6048 System Research & Information Technologies, 2019, № 3 48
tessence of the function fragment). One way or another the higher organism can-
not conduct an adequate functional informational activity, for example, without a
nervous system, a classic computer without a storage device, a camera without an
optical device, but with no doubt, you can try to hammer a nail or split a nut with
this camera.
Thus, it is defining the concept of the universality degree of a state which is
in a general sense is comparable to the concept of importance and in a particular
sense is inclined to gradual properties i.e. a tendency to functional concentration
or specialization or on the contrary a tendency to functional dispersion. A limit
PIG -type structures specialized on the one hand and common on the other, are
mainly expressed depending on the scale in the environment. At the same time,
the specialized function, as a special case of the general, is represented in the min-
imum permissible instance and is the quintessence of the functional information
state.
The target or informational affinity of vectors is determining by the measure
of the intersection of such vectors in the space of functions. The target similarity
of vectors is determined by the degree of the topological identity of such vectors
(which is usually accompanied by algorithmic similarity). Thus, the target or in-
formational similarities are not always related but are always similar algorithmi-
cally. Consequently, the similarity of structures regulating (which have affinity
respectively) states that perform similar functions is the higher, the higher the
similarity of the information purposes of such functions. In turn, the similarity of
state structures as functions of an informational purpose, which regulating states
that perform similar functions, the higher, the higher the similarity of information
goals of such functions and so on. In this interpretation, the gradual dependences
of the substrate’s states similarity and the information goals of their functions are
clearly manifested. The similarity of the environment structures seems to depend
on the functional-informational similarity of their purposes, where the measure of
similarity in both cases is the level of their algorithmic isomorphism.
Some states have special inducible properties when a disturbance, with
certain importance, in the structure of state S, occurs when there is a special
incoming signal 0>)(Si for S appears, and when 0)( =Si the signal is the
absence of a signal, respectively. All states are inducible. Therefore, we are
talking about a special induction component of the same special functional-
information property of the local state (the most important passing vectors). It is
assumed that each state has at least one special inducible attribute or vector.
The state of the i -potential for S regulation is the main cause of stability
and the general existence of systems in which they belong or the dynamics of the
sets which they induce. Such of mechanisms are probably the main and only
factor in the formation of coordinated behavior regulation of dissipative systems,
which, in turn, determine the dynamics of higher-order sets, etc.
GENERAL DYNAMIC OF SYSTEM
Each system attempts to establish sustainability, its own independence and integ-
rity on a scale, that forms the limit of visibility or some particular form of emer-
gence a as a contour of a separate system S . Even if the dynamics of S looks
and behaves according to absolute rest )(Sa (not receiving an impulse from out-
To the theory of systems: a brief look at the underlying of notions in the field …
Системні дослідження та інформаційні технології, 2019, № 3 49
side), there is always an active process x that is part of such a system Sx
even if such a process is not able to qualitatively affect on S and go beyond the
restriction a without external disturbances.
A stable functional state is a consequence, first of all, of the balance stability
in the structure of its set repetitions which is formed by functional cycles *)(xf
that come from the depths of the state (fig. 1). Deviations† (disturbance appear-
ance) in such cycles determine the balance point shift in the repeat state function
*)(xf the functional significance of which is dependent on the stability property
of a higher order system. During the system movement in scale, the forming in-
tervals on repetitions acquire differences only in the case of a certain exogenous
signal presence.
We can define nN as the set n of depth D in the flow P :
,N=n,, nkkk
n
=k
k ...
1
location of the cyclic function )(xf in a state S can be
displayed as .)()( (*)
1
(*)*
n
n
=k
kn xfNa Fig. 1 shows a functional movement of
four states that form a motion vector that transfers a stable state 1S to a stable
state 2S with an unstable structure, where the nested function )( 2
3f receives an
incoming destructive signal ,i γ )( 2 however, depending on the measure of the
functional circuit ( a ) stability that received such a signal is defining its further
existence and, consequently, the existence of higher functional circuits a when
aa . In this case, the function )( 2
3f acts as a property to prevent the
disintegration of the cyclic contour )( 2
31f even with the change in the function
)( 2
3f (the case when an intrafunctional replacement is carried out without a
qualitative change in the signal) algorithm and thereby completely leaving the
higher structures )( 2
31f , )( 2
31f intact. Degenerative functions, depending on
their synergistic potential, can initiate the disintegration of the functional state
with different speed or efficiency. Formally, fig. 1 displays the dynamics of the
action space as a continuous one-dimensional linear set in such a way that this set
is a reflection or map of the actions that are identical to the real environment. It
should be noted that this interpretation is very compatible with the description of
coupled mappings in distribution systems [7].
A destructive signal di is such if a destructive potential prevails in it and
a stabilizing one si is such if a stabilizing potential prevails in it, respectively.
Classical destructive processes are instability, for example, in autowaves, it mani-
fests itself in the formation of turbulence or instability and leading to the rupture
of the spirals.
di can have stabilizing qualities in some local relations while si destructive,
but one way or another di leads to functional destruction and si to functional
stability in some ,Nn providing there is no effective resistance of the environ-
ment that does not enable the distribution i out of a .
Vladimir P. Kolyada
ISSN 1681–6048 System Research & Information Technologies, 2019, № 3 50
The figure displays: nSSSS ,,, 210 — are states, when 1S is the repeat of 0S ;
2S is the iteration of 1S etc.; nN,,, — sets in the environmental scale, when
α;γ )()()( 313131 ƒ,ƒ,ƒ — ranges of cyclic stable function
)(:)())(( 1 )31( nn
n
k kn NiNN=xfP — is the sum of all qualitative repeats
)(xf of the flow P which retain the original signal; cb,a, — are the depths of
actions; τ — symmetric state (description below); , — outgoing and incoming
functional-information signals; nnn ,, β — noise that is not included in the func-
tional circuit; * — degenerative functions that reduce the stability of the system
Fig. 1. The diagram illustrates the dynamic features of the functional state in the envi-
ronmental movement process
To the theory of systems: a brief look at the underlying of notions in the field …
Системні дослідження та інформаційні технології, 2019, № 3 51
and leading to the rapid disintegration of a stable functional state; D — scale
(depth) of the environment; T — direction of the environment repeat genera-
tion or states map for the next time; P — flow direction;
,)(,)(( 10 21 S,SbS,SaP,T,D, .))( 2 nS,Sc
The state 1S can be considered as a qualitative segment of the state 0S repe-
tition, that did not receive di to some nN of the depth D or if such a signal was
received at the “safe” depth then the function that received the signal has full re-
sistance to it. This class of state repetitions seems to have the greater potential for
the complex system’s formation, the larger interval of D values beyond which
the probability in the formation of at least quality destructive signals for the cur-
rent system )(Da is reduced. For example, the state 2S has an incoming destruc-
tive signal ,i γd )*( 2 that does not have sufficient potential for a qualitative (non-
structural) effect on the function )( 2
3γf it happens so that the cyclic function
)( 2
31γf remains completely intact in relation to the higher functional cycle
)( 2
31f and state 2S can also be considered as a qualitative repetition of the
state 1S . In turn, the state nS is defined as unstable due to the fact that there is a
predominance of self-destructive and not self-stabilizing properties. )(* ),2( n
γdi ,
with sufficient potential destroys the functional circuit )( 31
nγf in such a way that
the newly synthesized interval nγN , due to its intact functions (functions that
have successfully repeated), still not able to qualitatively affect the
)()( yfα,f . At the same time, a similar situation can also occur in a higher
function )( n
nf with the only difference that, as a result of a destructive signal
,n
* the number of qualitative repetitions in it will not be enough to form
a functional circuit )( 31
nαf , which will lead to the complete destruction of the
interval on S and the development of a chaotic regime. With the help of a stabi-
lizing feedback signal )( n
si (or a signal having a local stabilizing potential), the
function )( n
nαf is quite capable of being qualitatively executed for 1+nS until
total destruction, when the structure of involved )( n
n
n
n γ,f becomes completely
inefficient in ensuring the synthesis of high-quality ))(( n
nαfS repetition.
The processes of a stable system SN , the synthesis of which can be carried
out by the intersection of certain cyclic (stable) sets mnS NN=N can also, to
some extent, be controlled by states nmN or other processes that somehow in-
volved in the operation of SN . That is, “relatives” of a local functional system,
the relatedness of which is the higher, the higher their functional predisposition to
such a system. Stable nmN type states with their algorithm can also initiate such a
stable system 1+SN that is able to regulatively influence their states-synthesizers
1+nmN . Stable states can be in balance† both with each other and with the nearest
medium and additively maintain stability through initiation and subsequent regu-
Vladimir P. Kolyada
ISSN 1681–6048 System Research & Information Technologies, 2019, № 3 52
lation of the synthesized states or diffuse recursive regulation of their own func-
tions and other dependent processes in the environment. An indicative and par-
ticular example of the described mechanism may be the biochemical functions of
the enzymatic intracellular starvation-saturation including extreme cases that lead
to the destruction of the system or cell death.
Processes of individual functional states may have closely related functions
or purposes. Previously, in this interpretation, it is worth to characterize the
concept of an information gradient (fig. 2) or a changing signal with respect to
1nN . This effect is a kind of information "fluctuation" with increasing of the
distance from the main function, where the fluctuation is expressed as the
dynamic q-parameter of the options set A of the function that triggers the signal
i , when )(Af=q , iAf )( . In this case, the targets )( nm Nii of the initial
state have the highest concentration (in the N space) and as the negative scaling
proceeds, this functional concentration decreases )( 1 nm<n Nii . The
concentration itself is quite similar to the potential function f for the Laplace
operator
2
2
x
f
on a one-dimensional vector space.
It is obvious that the higher the target f on axis SN from the state (at the
point nS ), the less the probability of this state inductions for f , which is natural
since the number of actions and the entropy factor increase. Consequently, a
similar situation arises in a related relation as a special case of q-parameter in the
space of functions.
In addition, as mentioned above, the vectors of closely related functions
intersect, and the measure of the relatedness of such functions depends on a
quantity of joint states for such vectors and how far these states from each other.
Such constellation intersections can form stable states nmN the number of which
becomes dependent on the probability of synthesis a high order steady state SN
f(Sn(Sn+1))
N
S
=
N
n
(S
n
)
Sn+1Sn-0.5 Sn
iim(Nn)
iin<m(Nn-1)
i
Fig. 2. Dotted arrows schematically indicate the direction of flow in the space of func-
tions, where the depth interval of such a space relatively corresponds to the axis of appli-
cate and indicated by a dotted line with the corresponding density
To the theory of systems: a brief look at the underlying of notions in the field …
Системні дослідження та інформаційні технології, 2019, № 3 53
when nmSS NNN )( . SN , in a particular strategy of self-organization, can have
reverse stabilizing signals into itself, ensuring sufficient resistance of the nmN to
degenerative factors. Thus, it is possible that dependencies running in a
specialized probabilistic situation (where the general noise level that including the
combined levels of uncertainty constitutes a process of states that contributes to
the synthesis and subsequent support for the performance of a certain function)
with a certain degree of recursion can be or become stable or important states
(such as in the regulation of prokaryotic operons [8]).
We can also highlight the phenomenon of the directional regulation, which is
a set of stable states vectors at the intersection of which is synthesizing a determi-
nistic state, which, in turn, with a high probability is also stable due to the predis-
position of any regulation to stability in principle. From the effectiveness of regu-
lation, the stability or steadiness of regulation is also determined, since regulation
itself can occur only in a stable and steadiness dynamic environment.
EVOLUTION FEATURES
The phenomenon of affinity may lead to evolutionary regulation and adjustment
of indicators of pseudo-probabilistic intersections as the environment moves. In
the first case, the signal with a regulating potential is maintained even under the
multiple transformations of the initiating state, and in the second case, the regula-
tion of affinity into itself that executed by the function |)(| xf .
The ability of complex systems to self-organize and adapt in short-term or
long-term (evolutionary) conditions is a natural response to environmental
variability. Short-term conditions may correspond in particular to the mechanisms
of the Belousov-Zhabotinsky reaction or biological embryonic induction-
differentiation. In turn, long-term conditions evolutionary phenomena of
allogenesis, aromorphosis or anagenesis, etc.
A particular case of long-term self-organization, which seems to have a
peak† importance indicator, is the phenomenon of evolutionary cephalization, that
reflecting a significant functional similarity between the individual biological
systems of an acceptable, higher taxonomic category and the evolutionary
movement under correlation factors over time. An artificially† induced adaptation
phenomenon can be, for example, the domestication of animals with the
subsequent restructuring of the organism's genome and the corresponding
phenotypic changes, which is also part of the evolutionary self-organization
mechanism.
Corresponding factor of the organization complicating that forming
evolutionary peaks in the environment, is an increasing the complexity of the
nested systems 1+nN (on a biological scale, this may be the differentiation of
individual cells, their groups, membrane, intracellular and other microsystems),
organization that synthesizing corresponded return signals of the external
environment 1nN and whose dynamic are also variative. Thus, it is possible to
define )(τi (see fig. 1) as a symmetric state in a quasi-space nI that inversely
complicates the functional-informational structure, which seems to be a crucial
part of the evolution strategy in the environment.
The processes of self-organization in all systems and in particular organisms
are represented most clearly in the form of protective mechanisms against exter-
nal and internal influences penetrating the system, increasing the risk of initiating
Vladimir P. Kolyada
ISSN 1681–6048 System Research & Information Technologies, 2019, № 3 54
destructive progress. In the process of evolution, each organism in any way de-
veloped a similar system of protection, more clearly in the form of specific inter-
nal biochemical reactions, or more generalized in the form of the strategy features
of the whole organism’s life cycle or their group. Immune-like processes in evolu-
tion, obviously modified in proportion to how the organisms themselves changed
their habitat and mainly increased the complexity of the system’s organization
(for example, CRISPR in prokaryotes, RNA interference (RNAi) in plants, or an
immune complex of protection against pathogenic effects in higher organisms
including humans).
We can conditionally divide the mechanisms of long-term self-organization
formed in evolution into two levels. The first is based on more direct dependen-
cies on the structure of the evolutionary movement, and the second level is form-
ing on the basis of indirect or consequence constellations of the first level or
states located closer to the periphery on the gradient plane of functional radiation
in the environment. If Immune-like systems belong to the first level of self-
organization, then at least all other functionally related processes (that are having
a much more significant stochastic origin indicator) can be attributed to the sec-
ond level of self-organization (for example, the phenomenon of allelic exclusion
in the regulation of the immune system B-cells differentiation [9, 10]). Anyway,
each mechanism having obvious signs of any first level self-organization is lo-
cated closer to the center of the functional radiation pattern, while the indirect or
second level is respectively located to the periphery.
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Received 10.04.2019
From the Editorial Board: the article corresponds completely to submitted manuscript.
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| id | journaliasakpiua-article-162809 |
| institution | System research and information technologies |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2025-07-17T10:24:29Z |
| publishDate | 2019 |
| publisher | The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" |
| record_format | ojs |
| resource_txt_mv | journaliasakpiua/4f/e058e4aa899b113b92f00cf652f7b04f.pdf |
| spelling | journaliasakpiua-article-1628092019-12-13T15:15:18Z To the theory of systems: a brief look at the underlying of notions in the field of conceptual content К теории систем: краткий обзор особенностей понятий в концептуальном поле До теорії систем: швидкий огляд особливостей понять в концептуальному полі Kolyada, Vladimir P. theory of systems notions universal evolution теория систем понятия универсальность эволюция теорія систем поняття універсальність еволюція From the systems theory point of view the attempting was made to establish the most suitable logical and semantical conceptual definition for systems notions while maintaining the maximal compatibility in the theoretical field, which enable to bring together systems with any scale and complexity to a single strategy of interpretation of their dynamics. The special semantic clarifications for notions which generating theoretical ground were established. Thus specified fundamental and system-forming processes. Direct relations of specific terms and subtleties of differences of system notions, their roles for creating solid theoretical representation were highlighted. Some examples of the biochemical types are given. An explicit, semantic clarification of some concepts describing the dynamics of systems and states is proposed. С системной точки зрения сделана попытка обнаружить наиболее подходящее логико-семантическое понятийное определение для системных понятий, сохраняя максимально допустимую совместимость на теоретической плоскости, позволяющую свести системы любого масштаба и сложности к единой стратегии в интерпретации их динамики. Установлены специальные семантические уточнения для понятий, образующих теоретические основание и тем самым конкретизированы фундаментальные системообразующие процессы. Выделена непосредственная связанность определенных терминов, показаны тонкости в различии таких системных понятий, их роль в формировании единого системного теоретического представления, приведены некоторые примеры биохимического типа. Предложено явное семантическое уточнение некоторых понятий, описывающих динамику систем и состояний. Із системної точки зору зроблено спробу виявити найбільш зручне логіко-семантичне понятійне визначення для системних понять зі збереженням максимально можливої сумісності на теоретичній площині, яка дає змогу звести системи будь-якого масштабу та складності в єдину стратегію інтерпретації їх динаміки. Установлено спеціальні семантичні уточнення для понять, які формують теоретичну основу, і тим самим конкретизовані фундаментальні системоформувальні процеси. Виділено безпосередню зв’язність деяких термінів, показано тонкощі у відмінностях таких системних понять, їх роль у формуванні єдиного системного теоретичного уявлення, наведено деякі приклади біохімічного типу. Запропоновано явне семантичне уточнення деяких понять, що характеризують динаміку систем та станів. The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2019-10-07 Article Article application/pdf https://journal.iasa.kpi.ua/article/view/162809 10.20535/SRIT.2308-8893.2019.3.04 System research and information technologies; No. 3 (2019); 41-54 Системные исследования и информационные технологии; № 3 (2019); 41-54 Системні дослідження та інформаційні технології; № 3 (2019); 41-54 2308-8893 1681-6048 en https://journal.iasa.kpi.ua/article/view/162809/183559 Copyright (c) 2021 System research and information technologies |
| spellingShingle | теорія систем поняття універсальність еволюція Kolyada, Vladimir P. До теорії систем: швидкий огляд особливостей понять в концептуальному полі |
| title | До теорії систем: швидкий огляд особливостей понять в концептуальному полі |
| title_alt | To the theory of systems: a brief look at the underlying of notions in the field of conceptual content К теории систем: краткий обзор особенностей понятий в концептуальном поле |
| title_full | До теорії систем: швидкий огляд особливостей понять в концептуальному полі |
| title_fullStr | До теорії систем: швидкий огляд особливостей понять в концептуальному полі |
| title_full_unstemmed | До теорії систем: швидкий огляд особливостей понять в концептуальному полі |
| title_short | До теорії систем: швидкий огляд особливостей понять в концептуальному полі |
| title_sort | до теорії систем: швидкий огляд особливостей понять в концептуальному полі |
| topic | теорія систем поняття універсальність еволюція |
| topic_facet | theory of systems notions universal evolution теория систем понятия универсальность эволюция теорія систем поняття універсальність еволюція |
| url | https://journal.iasa.kpi.ua/article/view/162809 |
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