Simulations Of Dynamical Characteristics For Memristive Circuits With Periodic Stimuli

By leading periodic stimulus into memristive circuit or replacing the oscillation sub–unit in memristive circuit, a periodic excitation memristive circuit can be built, upon which complex dynamical characteristics can be shown. Periodically excited memristive circuits are newly found by introducing the memristor and periodic stimulus into the existing chaotic circuits model, in which the complex nonlinear phenomena are revealed.An non–autonomous periodically excited fourth–order Chua’s memristive circuit is built by introducing a sinusoidal voltage stimulus into the existing fourth–order autonomous Chua’s memristive circuit. By utilizing theoretical formulations, simulations and experimental verification, the complex dynamics of the proposed circuit is investigated. Due to the added sinusoidal voltage stimulus, the equilibrium point of the circuit changes periodically versus time evolution, and equilibrium point switches between a line equilibrium and no equilibrium, resulting in the occurrence of self-excited attractor and hidden attractor alternatively. Moreover, some abundant interesting nonlinear phenomena including transient chaos, transient hyperchaos, chaotic beats are revealed.For the purpose of simplified the non–autonomous memristive circuit, a simple periodically driven MRLC circuit is proposed, which is constructed through replacing the Chua’s diode with an non–ideal active voltage–controlled memristor and leading a sinusoidal voltage stimulus into a variant of Murali–Lakshmnan–Chua circuit. Numerical simulations of the mathematical model and hardware experiments are performed, from which complex dynamical behaviors such as limit cycle oscillations, quasiperiodic attractors, and weak chaotic attractors are numerically simulated and experimentally captured. The results indicate that the complex dynamical behaviours of the newly proposed periodically driven memristive circuit are depending on parameters of the circuit and stimulus. The proposed circuit has the advantage of simpler structure and physical fabrication easily.