Coupling dynamics in an FHN bi-neuron model coupled via ReLU function-based locally active memristor

Locally active memristor (LAM) can exhibit memristive and locally active properties, which is a new candidate for generating complicity and assists us for emulating synapse functionalities. This paper uses a controllable ReLU function-based LAM as a memristive synapse to build a FitzHugh-Nagumo (FHN) bi-neuron model. Theoretical analysis shows that the equilibrium point and stability of the FHN bi-neuron model depend on parameters of the ReLU function-based LAM. Afterward, coupling dynamics, i.e., coexisting behavior and phase synchronization related to model parameters and memristor initial condition, are investigated by multiple numerical tools. Finally, a PSIM-based analog circuit is implemented and circuit simulations are performed to verify the correctness of the numerical simulations and the feasibility of the FHN bi-neuron circuit.