When a Neuron and its Self-Cascade System Coupled by a Memristor Synapse

The memristor can showcase the induced currents between neurons, serving as synapses that link two neural systems. At the same time, self-cascade operations yield new systems with original discrete dynamics. This paper proposes a hybrid construction method with coupling neuron system based on discrete memristor synapses and self-cascade operations. Rulkov and Chialvo neurons are employed as the foundation, and the coupled systems are analyzed. Two synchronous transitions are observed in the coupled system of Rulkov neurons, whereas new discharge patterns emerge in the hybrid coupling Chialvo neurons. The numerical simulations and theoretical analysis have been proved in the CH32 hardware platform.