Abstract: Based on the chaotic Rulkov neuron model, the two-parameter bifurcation analysis of the coupled Rulkov neuron model was carried out through numerical calculations  by considering the situation of two identical neurons under electrical coupling, and the bifurcation mode was further validated by using the one-parameter bifurcation diagrams and the maximum Lyapunov exponent diagrams. The results show that the coupled Rulkov neuron model exhibits three classic chaotic paths: period-doubling bifurcation path, quasi-periodic bifurcation path, and intermittency path. The model presents a period-adding bifurcation phenomena accompanied by chaos. The coupled Rulkov neurons model exhibits more complex dynamical behavior as the coupling strength increases.

Key words: Rulkov neuron, electrical coupling, two-parameter bifurcation analysis, the maximum Lyapunov exponent, chaotic path