A novel chaotic circuit with coexistence of multiple attractors and state transition based on two memristors

Abstract

A novel chaotic circuit that includes two memristors, an inductor, and a capacitor in parallel is planned, then the dimensionless mathematical model is built. Seven kinds of different attractors are found in the system. Using traditional dynamical analysis methods, the circuit system's equilibrium point and stability are analyzed, and under certain conditions, this system not only has infinite equilibrium points but also has no equilibrium point. Then, the dynamical behaviors with the changing parameter of the system are analyzed in-depth. A wealth of special phenomena has been discovered, such as the multi-state transition and the coexisting attractors. At last, the circuit system is implemented by using the DSP platform, and the theoretical analysis is verified by the results. Theoretical analysis and simulation results show this novel memristive chaotic system has abundant dynamic behaviors. Based on these abundant dynamical characteristics and its self-excited attractors or hidden attractors under different conditions, this circuit system has the potential application in secure communication and image encryption.