Initial-Boosted Behaviors and Synchronization of Memristor-Coupled Memristive Systems

Because of the special nonlinearity with inner states, memristors can induce the initial-condition-dependent extreme multistability in their constituent systems. However, when the memristor is taken as a coupler to synchronize two identical memristive systems, what synchronous behaviors could be achieved? So far, it has not been comprehensively concerned in literature. To this end, this paper presents a 9-D memristor-coupled system consisting of two homogenous memristive systems and studies its initial-boosted dynamics and synchronous behaviors. Dynamics evolutions related to the coupling memristor and two subsystem memristors are elaborated. Using Lyapunov's stability theorem, the synchronicities of the initial-condition-sensitive dynamics are demonstrated theoretically. Furthermore, based on the integral transformation model, the synchronization parameter regions are estimated quantitatively using a newly proposed variable-parameter conversion method. Thereafter, various coexisting synchronous behaviors are discovered by tuning the memristor initial conditions and verified via the microcontroller-based hardware measurements. It is demonstrated that the memristor coupler provides a flexible control scheme for the synchronization of memristive systems.