Bifurcation delay in a network of nonlocally coupled slow-fast FitzHugh–Nagumo neurons

Abstract

Many slow-fast systems can exhibit delayed bifurcation, which means that the crucial transition occurs after some delay during the transition between the oscillatory and steady states due to the presence of a slowly varying parameter. We specifically analyze the dynamical behavior of bifurcation delay in a network of nonlocally coupled FitzHugh–Nagumo neurons by adjusting the frequency of slowly varying currents. Interestingly, we observe an appearance of chimera-like states despite a tiny parameter mismatch in the frequency of any single node. The observed chimera-like state is evidenced through the mean-phase velocity profile. The robustness of the obtained results is then tested by perturbing multiple neurons in three different ways: constant, linearly increasing, and decreasing frequency of certain nodes. Importantly, we discover that the observed chimera state is resilient to all perturbations.