Dynamics of a random Hopfield neural lattice model with adaptive synapses and delayed Hebbian learning
UDC 517.9 A Dong–Hopfield neural lattice model with random external forcing and delayed response to the evolution of interconnection weights is developed and studied.   The interconnection weights evolve according to the Hebbian learning rule with a decay term and contribut...
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| Date: | 2024 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2024
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/7594 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 517.9
A Dong–Hopfield neural lattice model with random external forcing and delayed response to the evolution of interconnection weights is developed and studied.   The interconnection weights evolve according to the Hebbian learning rule with a decay term and contribute to  changes in the states after a short delay.  The lattice system is  first reformulated as a coupled functional-ordinary differential equation system on an appropriate product space.  Then the solution of the system is shown to exist and be unique. Furthermore  it is shown that the system of equations  generates a continuous random dynamical system.  Finally, the existence of random attractors for the random dynamical system generated by the Dong–Hopfield model is established. |
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| DOI: | 10.3842/umzh.v75i12.7594 |