EVANS FUNCTIONS AND BIFURCATIONS OF STANDING WAVE SOLUTIONS IN DELAYED SYNAPTICALLY COUPLED NEURONAL NETWORKS

Linghai Zhang

doi:10.11948/2012016

2012 Volume 2 Issue 2

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Linghai Zhang. EVANS FUNCTIONS AND BIFURCATIONS OF STANDING WAVE SOLUTIONS IN DELAYED SYNAPTICALLY COUPLED NEURONAL NETWORKS[J]. Journal of Applied Analysis & Computation, 2012, 2(2): 213-240. doi: 10.11948/2012016

Citation:

Linghai Zhang. EVANS FUNCTIONS AND BIFURCATIONS OF STANDING WAVE SOLUTIONS IN DELAYED SYNAPTICALLY COUPLED NEURONAL NETWORKS[J]. Journal of Applied Analysis & Computation, 2012, 2(2): 213-240. doi: 10.11948/2012016

EVANS FUNCTIONS AND BIFURCATIONS OF STANDING WAVE SOLUTIONS IN DELAYED SYNAPTICALLY COUPLED NEURONAL NETWORKS

Linghai Zhang

Department of Mathematics, Lehigh University, 14 East Packer Avenue, Bethlehem, PA 18015, USA

Abstract

Abstract

Consider the following nonlinear singularly perturbed system of integral differential equations
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and the scalar integral differential equation
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There exist standing wave solutions to the nonlinear system. Similarly, there exist standing wave solutions to the scalar equation.
The author constructs Evans functions to establish stability of the standing wave solutions of the scalar equation and to establish bifurcations of the standing wave solutions of the nonlinear system.
- Delayed synaptically coupled neuronal networks /
- standing wave solutions /
- existence /
- stability /
- instability /
- bifurcations /
- eigenvalue problems /
- Evans functions
MSC: 92C20

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