Initials-dependent dynamics and synchronization in a memristor coupled memristive map

Due to the unique nonlinearity with inner states, coupling memristors can make the subsystems to generate initials-dependent dynamical evolutions and synchronization behaviors in memristive networks, thus providing guidance for engineering applications. To this end, this paper designs a discrete model of the memristor-coupled memristive map composed of two identical memristive maps and a memristor coupler, and focuses on the initials-dependent dynamics and synchronizations. The coupling model exhibits a collection of spatial fixed points, whose stability depends on the initial states of the two subsystem memristors and the coupled memristor. On this basis, extreme multistability appears as symmetric coexisting attractors and dynamical distributions. The synchronization transitions and the phase synchronization with different kinds of phase errors are elaborated, which shows the synchronization effect of the coupling intensity and initial states. The results clarify that this coupling model can exhibit initials-dependent dynamics and synchronicity behaviors under the influence of three memristors. Afterwards, an FPGA-based hardware platform is used to verify the correctness of numerical simulations.