Dynamics of non–identical coupled Chialvo neuron maps

Abstract

We study numerically the dynamics of low–dimensional ensembles of discrete neuron models - Chialvo maps. We are focused on choosing the autonomous map parameters corresponding to the invariant curve. We consider two cases of coupling organization: (i) via a nonlinear function of models; (ii) linear coupling, which is an analog of electrical neuron interaction. For the first case, the possibility of invariant curve doublings and the emergence of quasi-periodicity within Arnold tongues as a result of the secondary Neimark-Sacker bifurcation are found. For the second case, we discover an area of three-frequency quasi-periodicity for the case of two neurons. It arises softly as a result of quasi-periodic Hopf bifurcation. We demonstrate a set of resonant two-frequency regimes tongues embedded in this area and bounded by lines of saddle-node bifurcations of invariant curves. For ensemble of three linearly coupled maps, four-frequency quasi-periodicity becomes possible with a built-in system of tongues of three-frequency regimes (tori). We discuss the effect of noise and the evolution of “noise quasi-periodic” regimes, resonant regimes of this type and bifurcations of invariant tori with increasing of noise intensity.