Stability and Oscillation of the Solutions for a Coupled FHN Model with Time Delays

A FitzHugh–Nagumo (FHN) model with delayed coupling is considered to investigate the stability and oscillatory behavior of the solutions due to the coupling strength and delay. Two theorems of sufficient conditions are given to guarantee the stability and oscillation of the solutions by constructing of Liapunov functional and applying the Chafee’s limit cycle criterion. Computer simulations are provided to illustrate the correctness of our theoretical analysis. Some results in the literature about coupled FHN systems are extended.

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