A self-symmetric cycle in a system of two diffusely connected Hutchinson's equations

The so-called bi-local model is considered for Hutchinson's equation. This is a system of two identical nonlinear delay differential equations connected by means of linear diffusion terms. The question of the existence, asymptotic behaviour and stability of a particular periodic solution of thi...

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Bibliographic Details
Published in:Sbornik. Mathematics 2019-02, Vol.210 (2), p.184-233
Main Authors: Glyzin, S. D., Kolesov, A. Yu, Rozov, N. Kh
Format: Article
Language:English
Subjects:
asymptotic behaviour
Asymptotic properties
bi-local model
Differential equations
Hutchinson's equation
Nonlinear equations
self-symmetric cycle
stability
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Summary:The so-called bi-local model is considered for Hutchinson's equation. This is a system of two identical nonlinear delay differential equations connected by means of linear diffusion terms. The question of the existence, asymptotic behaviour and stability of a particular periodic solution of this system, such that a certain phase shift takes the coordinates of this solution back to this solution, are investigated. Bibliography: 19 titles.
ISSN:1064-5616
1468-4802
DOI:10.1070/SM8941