Dynamics of FitzHugh-Nagumo excitable systems with delayed coupling

Abstract

Small lattices of $N$ nearest neighbor coupled excitable FitzHugh-Nagumo systems, with time-delayed coupling are studied, and compared with systems of FitzHugh-Nagumo oscillators with the same delayed coupling. Bifurcations of equilibria in N=2 case are studied analytically, and it is then numerically confirmed that the same bifurcations are relevant for the dynamics in the case $N>2$. Bifurcations found include inverse and direct Hopf and fold limit cycle bifurcations. Typical dynamics for different small time-lags and coupling intensities could be excitable with a single globally stable equilibrium, asymptotic oscillatory with symmetric limit cycle, bi-stable with stable equilibrium and a symmetric limit cycle, and again coherent oscillatory but non-symmetric and phase-shifted. For an intermediate range of time-lags inverse sub-critical Hopf and fold limit cycle bifurcations lead to the phenomenon of oscillator death. The phenomenon does not occur in the case of FitzHugh-Nagumo oscillators with the same type of coupling.

accepted by Phys.Rev.E

References in corpus (4)

• The World of the Complex Ginzburg-Landau Equation
• Time Delay in the Kuramoto Model of Coupled Oscillators
• Time Delay Induced Death in Coupled Limit Cycle Oscillators
• Time Delay Effects on Coupled Limit Cycle Oscillators at Hopf Bifurcation

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