## Abstract and Applied Analysis

### Stability Switches and Hopf Bifurcation in a Coupled FitzHugh-Nagumo Neural System with Multiple Delays

#### Abstract

A FitzHugh-Nagumo (FHN) neural system with multiple delays has been proposed. The number of equilibrium point is analyzed. It implies that the neural system exhibits a unique equilibrium and three ones for the different values of coupling weight by employing the saddle-node bifurcation of nontrivial equilibrium point and transcritical bifurcation of trivial one. Further, the stability of equilibrium point is studied by analyzing the corresponding characteristic equation. Some stability criteria involving the multiple delays and coupling weight are obtained. The results show that the neural system exhibits the delay-independence and delay-dependence stability. Increasing delay induces the stability switching between resting state and periodic activity in some parameter regions of coupling weight. Finally, numerical simulations are taken to support the theoretical results.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 874701, 13 pages.

Dates
First available in Project Euclid: 27 February 2015

https://projecteuclid.org/euclid.aaa/1425048233

Digital Object Identifier
doi:10.1155/2014/874701

Mathematical Reviews number (MathSciNet)
MR3232869

Zentralblatt MATH identifier
07023237

#### Citation

Yao, Shengwei; Tu, Huonian. Stability Switches and Hopf Bifurcation in a Coupled FitzHugh-Nagumo Neural System with Multiple Delays. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 874701, 13 pages. doi:10.1155/2014/874701. https://projecteuclid.org/euclid.aaa/1425048233

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