Volterra quadratic stochastic operators of a two-sex population
We introduce the notion of Volterra quadratic stochastic operators of a bisexual population. The description of the fixed points of Volterra quadratic stochastic operators of a bisexual population is reduced to the description of the fixed points of Volterra-type operators. Several Lyapunov function...
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| Date: | 2011 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2011
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/2779 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | We introduce the notion of Volterra quadratic stochastic operators of a bisexual population. The description of
the fixed points of Volterra quadratic stochastic operators of a bisexual population is reduced to the description
of the fixed points of Volterra-type operators. Several Lyapunov functions are constructed for the Volterra
quadratic stochastic operators of a bisexual population. By using these functions, we obtain an upper bound
for the ω-limit set of trajectories. It is shown that the set of all Volterra quadratic stochastic operators of a
bisexual population is a convex compact set, and the extreme points of this set are found. Volterra quadratic
stochastic operators of a bisexual population that have a 2-periodic orbit (trajectory) are constructed. |
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