Dynamic behavior in memristor coupled Hindmarsh–Rose and Fitzhugh–Nagumo neurons with synaptic crosstalk

Synaptic crosstalk is ubiquitous in many brain regions, but its effect on firing activities of neural network has rarely been studied. In this study, a heterogeneous neural network constructed with one Hindmarsh–Rose neuron model and one Fitzhugh–Nagumo neuron model is developed, in which the synaptic crosstalk is emulated by two mutually coupled memristors. The effect of crosstalk intensities on the firing activities of the neural network are discussed by time series, phase diagrams, Lyapunov exponents, and dynamic mapping. For different crosstalk intensities, the coexisting periodic firing and chaotic firing, the coexisting periodic firing and periodic firing, the coexisting chaotic firing and periodic firing, and the coexisting chaotic firing and chaotic firing are observed in the neural network under different memristor’s initial values. Furthermore, the effect of crosstalk intensity on synchronous firing between two neurons is also revealed and it is found that the two heterogeneous neurons transit from initially oscillate independently to gradually achieve fully synchronous firing behavior as the crosstalk intensities decrease. Finally, the numerical simulations are verified by circuit simulation experiment based on Multisim.