Relaxation Oscillations in a System of Two Pulsed Synaptically Coupled Neurons
We consider a mathematical model of synaptic interaction between two pulse neuron elements. Each of the neurons is modeled by a singularly-perturbed difference-differential equation with delay. Coupling is assumed to be at the threshold, and time delay is taken into consideration. Problems of existe...
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| Format: | Article |
| Language: | English |
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Yaroslavl State University
2017-02-01
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| Series: | Моделирование и анализ информационных систем |
| Subjects: | |
| Online Access: | https://www.mais-journal.ru/jour/article/view/427 |
| _version_ | 1826559085303037952 |
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| author | Sergei D. Glyzin Andrey Yu. Kolesov Elena A. Marushkina |
| author_facet | Sergei D. Glyzin Andrey Yu. Kolesov Elena A. Marushkina |
| author_sort | Sergei D. Glyzin |
| collection | DOAJ |
| description | We consider a mathematical model of synaptic interaction between two pulse neuron elements. Each of the neurons is modeled by a singularly-perturbed difference-differential equation with delay. Coupling is assumed to be at the threshold, and time delay is taken into consideration. Problems of existence and stability of relaxation periodic movements for obtained systems are considered. It turns out that the ratio between the delay due to internal causes in a single neuron model and the delay in the coupling link between oscillators is crucial. Existence and stability of a uniform cycle of the problem is proved for the case where the delay in the link is less than a period of a single oscillator that depends on the internal delay. As the delay grows, the in-phase regime becomes more complex, particularly, it is shown that by choosing a suitable delay, we can obtain more complex relaxation oscillation and inside a period interval the system can exhibit not one but several high-amplitude splashes. This means that bursting-effect can appear in a system of two synaptic coupled oscillators of neuron type due to a delay in a coupling link. |
| first_indexed | 2024-04-10T02:26:01Z |
| format | Article |
| id | doaj.art-5db732643307430ea67b5543b4b6c3de |
| institution | Directory Open Access Journal |
| issn | 1818-1015 2313-5417 |
| language | English |
| last_indexed | 2025-03-14T08:54:47Z |
| publishDate | 2017-02-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj.art-5db732643307430ea67b5543b4b6c3de2025-03-02T12:46:50ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172017-02-01241829310.18255/1818-1015-2017-1-82-93354Relaxation Oscillations in a System of Two Pulsed Synaptically Coupled NeuronsSergei D. Glyzin0Andrey Yu. Kolesov1Elena A. Marushkina2P.G. Demidov Yaroslavl State University; Scientific Center in Chernogolovka RASP.G. Demidov Yaroslavl State UniversityP.G. Demidov Yaroslavl State UniversityWe consider a mathematical model of synaptic interaction between two pulse neuron elements. Each of the neurons is modeled by a singularly-perturbed difference-differential equation with delay. Coupling is assumed to be at the threshold, and time delay is taken into consideration. Problems of existence and stability of relaxation periodic movements for obtained systems are considered. It turns out that the ratio between the delay due to internal causes in a single neuron model and the delay in the coupling link between oscillators is crucial. Existence and stability of a uniform cycle of the problem is proved for the case where the delay in the link is less than a period of a single oscillator that depends on the internal delay. As the delay grows, the in-phase regime becomes more complex, particularly, it is shown that by choosing a suitable delay, we can obtain more complex relaxation oscillation and inside a period interval the system can exhibit not one but several high-amplitude splashes. This means that bursting-effect can appear in a system of two synaptic coupled oscillators of neuron type due to a delay in a coupling link.https://www.mais-journal.ru/jour/article/view/427neural modelsdifferential-difference equationsrelaxation oscillationsasymptotic behaviorstabilitysynaptic coupling |
| spellingShingle | Sergei D. Glyzin Andrey Yu. Kolesov Elena A. Marushkina Relaxation Oscillations in a System of Two Pulsed Synaptically Coupled Neurons Моделирование и анализ информационных систем neural models differential-difference equations relaxation oscillations asymptotic behavior stability synaptic coupling |
| title | Relaxation Oscillations in a System of Two Pulsed Synaptically Coupled Neurons |
| title_full | Relaxation Oscillations in a System of Two Pulsed Synaptically Coupled Neurons |
| title_fullStr | Relaxation Oscillations in a System of Two Pulsed Synaptically Coupled Neurons |
| title_full_unstemmed | Relaxation Oscillations in a System of Two Pulsed Synaptically Coupled Neurons |
| title_short | Relaxation Oscillations in a System of Two Pulsed Synaptically Coupled Neurons |
| title_sort | relaxation oscillations in a system of two pulsed synaptically coupled neurons |
| topic | neural models differential-difference equations relaxation oscillations asymptotic behavior stability synaptic coupling |
| url | https://www.mais-journal.ru/jour/article/view/427 |
| work_keys_str_mv | AT sergeidglyzin relaxationoscillationsinasystemoftwopulsedsynapticallycoupledneurons AT andreyyukolesov relaxationoscillationsinasystemoftwopulsedsynapticallycoupledneurons AT elenaamarushkina relaxationoscillationsinasystemoftwopulsedsynapticallycoupledneurons |