Hidden extreme multistability and synchronicity of memristor-coupled non-autonomous memristive Fitzhugh-Nagumo models

When taking a memristor as a coupler to connect two memristive systems, the intricate initial condition-dependent coexisting and synchronous behaviors could be achieved, which have not been comprehensively concerned in literature. This work presents a memristor-coupled homogeneous network consisting of two identical non-autonomous memristive Fitzhugh-Nagumo models and investigates its coexisting and synchronous behaviors. Kinetic analysis shows that the network can exhibit hidden extreme multistability similar to that of the individual non-autonomous memristive Fitzhugh-Nagumo model. Coexisting hidden hyperchaotic, chaotic, periodic, and quasi-periodic attractors are numerically revealed, and their synchronicities are controlled by the initial condition and coupling strength of the coupling memristor. The synchronous effects of the coupling strength and initial conditions of the network are numerically revealed using normalized mean synchronization errors. Complete and parallel-offset synchronous behaviors are realized with a large positive coupling strength and a negative initial condition of the coupling memristor. In addition to these two synchronous behaviors, phase synchronization is easily achieved due to the existence of external stimuli. These synchronous states are flexibly controlled by the initial conditions. Furthermore, an analog circuit is designed for the memristor-coupled homogenous network and circuit simulations are performed to verify the numerical results.