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Periodic solutions of planar systems with two delays

Published online by Cambridge University Press:  14 November 2011

Shigui Ruan  and
Junjie Wei
Shigui Ruan
Affiliation:
Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5
Junjie Wei
Affiliation:
Department of Mathematics, Northeast Normal University, Changchun, Jilin 130024, People's, Republic of China
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Abstract

In this paper, we consider a planar system with two delays:

ẋ1(t) = −a0x1(t) + a1F1 (x1(t − τ1), x2(τ−t2)).

ẋ2(t) = −b0x2(t) + b1F2 (x1(t − τ1), x2(t − τxs2)).

Firstly, linearized stability and local Hopf bifurcations are studied. Then, existence conditions for non-constant periodic solutions are derived using degree theory methods. Finally, a simple neural network model with two delays is analysed as an example.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 129 , Issue 5 , 1999 , pp. 1017 - 1032
Copyright
Copyright © Royal Society of Edinburgh 1999

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