SELF-EXCITED WAVE PROCESSES IN CHAINS OF UNIDIRECTIONALLY COUPLED IMPULSE NEURONS
The article is devoted to the mathematical modeling of neural activity. We propose new classes of singularly perturbed differential-difference equations with delay of Volterra type. With these systems, the models as a single neuron or neural networks are described. We study attractors of ring system...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Yaroslavl State University
2015-06-01
|
| Series: | Моделирование и анализ информационных систем |
| Subjects: | |
| Online Access: | https://www.mais-journal.ru/jour/article/view/259 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | The article is devoted to the mathematical modeling of neural activity. We propose new classes of singularly perturbed differential-difference equations with delay of Volterra type. With these systems, the models as a single neuron or neural networks are described. We study attractors of ring systems of unidirectionally coupled impulse neurons in the case where the number of links in the system increases indefinitely. In order to study periodic solutions of travelling wave type of this system, some special tricks are used which reduce the existence and stability problems for cycles to the investigation of auxiliary system with impulse actions. Using this approach, we establish that the number of stable self-excited waves simultaneously existing in the chain increases unboundedly as the number of links of the chain increases, that is, the well-known buffer phenomenon occurs. |
|---|---|
| ISSN: | 1818-1015 2313-5417 |