On the Number of Coexisting Autowaves in the Chain of Coupled Oscillators
We consider a model of neuron complex formed by a chain of diffusion coupled oscillators. Every oscillator simulates a separate neuron and is given by a singularly perturbed nonlinear differential-difference equation with two delays. Oscillator singularity allows reduction to limit system without sm...
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| Format: | Article |
| Language: | English |
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Yaroslavl State University
2014-10-01
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| Series: | Моделирование и анализ информационных систем |
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| Online Access: | https://www.mais-journal.ru/jour/article/view/92 |
| _version_ | 1826558963435438080 |
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| author | Y. V. Bogomolov S. D. GlyzinA A. Yu. Kolesov |
| author_facet | Y. V. Bogomolov S. D. GlyzinA A. Yu. Kolesov |
| author_sort | Y. V. Bogomolov |
| collection | DOAJ |
| description | We consider a model of neuron complex formed by a chain of diffusion coupled oscillators. Every oscillator simulates a separate neuron and is given by a singularly perturbed nonlinear differential-difference equation with two delays. Oscillator singularity allows reduction to limit system without small parameters but with pulse external action. The statement on correspondence between the resulting system with pulse external action and the original oscillator chain gives a way to demonstrate that under consistent growth of the chain node number and decrease of diffusion coefficient we can obtain in this chain unlimited growth of its coexistent stable periodic orbits (buffer phenomenon). Numerical simulations give the actual dependence of the number of stable orbits on the diffusion parameter value. |
| first_indexed | 2024-04-10T02:24:46Z |
| format | Article |
| id | doaj.art-4e5a2d41cdb34902b9b22be4b50a0594 |
| institution | Directory Open Access Journal |
| issn | 1818-1015 2313-5417 |
| language | English |
| last_indexed | 2025-03-14T08:52:50Z |
| publishDate | 2014-10-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj.art-4e5a2d41cdb34902b9b22be4b50a05942025-03-02T12:46:56ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172014-10-0121516218010.18255/1818-1015-2014-5-162-18086On the Number of Coexisting Autowaves in the Chain of Coupled OscillatorsY. V. Bogomolov0S. D. GlyzinA1A. Yu. Kolesov2P.G. Demidov Yaroslavl State UniversityP.G. Demidov Yaroslavl State University; Scientific Center in Chernogolovka RASP.G. Demidov Yaroslavl State UniversityWe consider a model of neuron complex formed by a chain of diffusion coupled oscillators. Every oscillator simulates a separate neuron and is given by a singularly perturbed nonlinear differential-difference equation with two delays. Oscillator singularity allows reduction to limit system without small parameters but with pulse external action. The statement on correspondence between the resulting system with pulse external action and the original oscillator chain gives a way to demonstrate that under consistent growth of the chain node number and decrease of diffusion coefficient we can obtain in this chain unlimited growth of its coexistent stable periodic orbits (buffer phenomenon). Numerical simulations give the actual dependence of the number of stable orbits on the diffusion parameter value.https://www.mais-journal.ru/jour/article/view/92difference-differential equationsrelaxation cycleautowavesstabilitybufferingbursting |
| spellingShingle | Y. V. Bogomolov S. D. GlyzinA A. Yu. Kolesov On the Number of Coexisting Autowaves in the Chain of Coupled Oscillators Моделирование и анализ информационных систем difference-differential equations relaxation cycle autowaves stability buffering bursting |
| title | On the Number of Coexisting Autowaves in the Chain of Coupled Oscillators |
| title_full | On the Number of Coexisting Autowaves in the Chain of Coupled Oscillators |
| title_fullStr | On the Number of Coexisting Autowaves in the Chain of Coupled Oscillators |
| title_full_unstemmed | On the Number of Coexisting Autowaves in the Chain of Coupled Oscillators |
| title_short | On the Number of Coexisting Autowaves in the Chain of Coupled Oscillators |
| title_sort | on the number of coexisting autowaves in the chain of coupled oscillators |
| topic | difference-differential equations relaxation cycle autowaves stability buffering bursting |
| url | https://www.mais-journal.ru/jour/article/view/92 |
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