Stable Relaxation Cycle in a Bilocal Neuron Model

We consider the so-called bilocal neuron model, which is a special system of two nonlinear delay differential equations coupled by linear diffusion terms. The system is invariant under the interchange of phase variables. We prove that, under an appropriate choice of parameters, the system under stud...

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Bibliographic Details
Published in:Differential equations 2018-10, Vol.54 (10), p.1285-1309
Main Authors: Glyzin, S. D., Kolesov, A. Yu, Rozov, N. Kh
Format: Article
Language:English
Subjects:
Analysis
Difference and Functional Equations
Differential equations
Mathematics
Mathematics and Statistics
Neurons
Nonlinear equations
Ordinary Differential Equations
Partial Differential Equations
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Summary:We consider the so-called bilocal neuron model, which is a special system of two nonlinear delay differential equations coupled by linear diffusion terms. The system is invariant under the interchange of phase variables. We prove that, under an appropriate choice of parameters, the system under study has a stable relaxation cycle whose components turn into each other under a certain phase shift.
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266118100026