Coexisting hyperchaos and multistability in a discrete memristor-coupled bi-neuron model

Memristor is a nonlinear electronic component with good plasticity, and it is widely used to function as the synapse. Significantly, the inter-neuronal communication is a discrete process via neurotransmitter, and the discrete memristor is suitable to emulate its dynamics. With the introduction of discrete memristors, the discrete neural models coupled with memristors have received widespread attention. In this paper, we present a one-dimensional (1D) Chialvo map, and a discrete memristor-coupled Chialvo neuron (DMCCN) map is designed by bidirectionally coupling two 1D Chialvo maps through a discrete memristor. The DMCCN map exhibits a linear fixed point set dependent on the initial condition of the memristor, and the stability is discussed. The dynamical behaviors are investigated through Lyapunov exponents (LEs), bifurcation diagrams, phase portraits, and firing patterns. The results indicate that the DMCCN map generates complex dynamical behaviors, such as chaos, hyperchaos and coexisting firing patterns. Specifically, these behaviors are highly dependent on the initial conditions, leading to initial-induced heterogeneous multistability and initial-boosted homogeneous multistability. Furthermore, a hardware circuit based on the DSP platform is designed to implement the DMCCN map, verifying its application potential.