Coexisting phenomena and antimonotonic evolution in a memristive Shinriki circuit

This paper is aimed at investigating the dynamical behaviors of the Shinriki circuit with a grounded asymmetric diode-bridge-based memristor through the implicit mapping method, including coexisting phenomena and antimonotonicity. To elucidate these behaviors, the basic properties, including equilibrium points and symmetry, of a Shinriki circuit incorporating a grounded asymmetric diode-bridge-based memristor are first illustrated. The discretization scheme for the circuit is established through the implicit mapping method, and the relatively complete bifurcation trees of each periodic motion by tuning a variable resistor can be analyzed through the Newton-Raphson algorithm. The unique unstable periodic bifurcation routes are also revealed. The evolution of antimonotonicity triggered by period-doubling or saddle-node bifurcations, along with the formed unstable motions, are comprehensively discussed. Furthermore, the simulation results are verified via a Field Programmable Gate Array (FPGA), by which both the asymmetric stable and unstable coexisting periodic attractors can be captured. The results will contribute to explaining the dynamical behaviors of numerous memristive circuits from a novel semi-analytical way, thus opening the possibility of analyzing some phenomena, such as unstable bifurcation routes, that cannot be directly observed via the numerical method.