Coexisting multiple firing behaviors of fractional-order memristor-coupled HR neuron considering synaptic crosstalk and its ARM-based implementation

Abstract

The crosstalk between synapses has a far-reaching impact on the specificity of synaptic communication in human brain. Therefore, the influence of synaptic crosstalk on the dynamic behaviors of neural network cannot be ignored. In this paper, we investigate the dynamics of fractional-order (FO) memristor-coupled Hindmarsh-Rose (HR) neuron model considering synaptic crosstalk. Firstly, the equilibrium points and stability are investigated via qualitative analysis, from which it can be obtained that the number and stability of equilibrium points have diversity for different crosstalk strength parameters. Secondly, the global coexistence of multiple firing patterns is reflected by phase diagrams, Lyapunov exponent spectrums and bifurcation diagrams. The local attraction basins reveal the multi-stability phenomenon related to the initial value. The parameter related firing behaviors are described by the two-parameter bifurcation diagram. In particular, the model shows the offset boosting control method for a single variable. Then, spectral entropy (SE) and C0 complexity chaos diagram are used to observe the change of system complexity when two parameters change simultaneously. Finally, the digital implementations based on ARM are given to verify the consistency with the numerical simulation results.