Dynamics of non–identical coupled Chialvo neuron maps

Chaos, Solitons and Fractals. 2024. Vol. 186. Article 115237.

Kuznetsov A. P., Sedova Y. V., Stankevich N.

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.

Keywords: хаос, chaos, показатели Ляпунова, Lyapunov exponents, Chialvo map, coupled maps, multi-frequency oscillations, отображение Киалво, связанные отображения, многочастотные колебания