Stability and chaos of Rulkov map-based neuron network with electrical synapse

•Stability of fixed points of two identical Rulkov map-based neurons coupled by the electrical synapses is obtained.•Chaos in the sense of Marotto is proved in a strict mathematical way.•These results could be useful for building-up large-scale neuron networks.

In this paper, stability and chaos of a simple system consisting of two identical Rulkov map-based neurons with the bidirectional electrical synapse are investigated in detail. On the one hand, as a function of control parameters and electrical coupling strengthes, the conditions for stability of fixed points of this system are obtained by using the qualitative analysis. On the other hand, chaos in the sense of Marotto is proved by a strict mathematical way. These results could be useful for building-up large-scale neurons networks with specific dynamics and rich biophysical phenomena.