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Yao, Shengwei; Tu, Huonian

Stability switches and Hopf bifurcation in a coupled FitzHugh-Nagumo neural system with multiple delays. (English) Zbl 1474.34488

Abstr. Appl. Anal. 2014, Article ID 874701, 13 p. (2014).
Summary: 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.

Cited in 4 Documents

MSC:

34K18 Bifurcation theory of functional-differential equations
92C20 Neural biology
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