Synchronization Dynamics of Two Heterogeneous Chaotic Rulkov Neurons with Electrical Synapses

Abstract

Two heterogeneous chaotic Rulkov neurons with electrical synapses are investigated in this paper. First, we study the ability of the second neuron to modify the dynamics of the first neuron. It is shown that when the parameters of the first neuron are located at the vicinity of the Neimark–Sacker bifurcation curves the first firing neuron can be controlled into the quiescent state when coupled with the second neuron. While the parameters of the first neuron are near the flip bifurcation curves the first firing neuron cannot be suppressed. Second, we discuss burst synchronization for two bursting neurons and two tonic spiking neurons. It is shown that two heterogeneous chaotic Rulkov neurons with tonic spiking firing cannot reach anti-phase synchronization under the inhibitory coupling, which is different from the property of nonchaotic Rulkov neurons. Finally, we show that for two bursting neurons if the coupling is strong enough then burst synchronization can be converted into spike synchronization. However, complete synchronization cannot be achieved for any strong coupling.