Abstract
The memristor-based chaotic system shows complex dynamical behaviors, which make it have a broader prospect in the fields of image encryption and signal processing. In this paper, a novel chaotic circuit with double memristors is proposed and the corresponding mathematical model is established through the flux-charge analysis method. Five adjustable constants in the flux-charge model are applied to describe the initial values of capacitance, inductance and memristor, so as to realize the physical control of multistability in hardware circuit. The number of equilibrium points in flux-charge domain is limited, and its stability is determined by the system parameters and five adjustable constants. Moreover, the coexisting bifurcation behaviors and the sensitivity of the system to initial values are analyzed through bifurcation diagrams and Lyapunov exponents. The coexistence of infinitely many attractors are investigated by basins of attraction, and the memristor-based system with different initial values displays stable points, periodic motions with different limit cycles, chaos and so on. Finally, the adaptive sliding mode controller is designed to complete the adaptive synchronization of two dual-memristor systems with unknown parameters under the influence of external disturbances, and the appropriate update laws are proposed to identify the unknown parameters successfully. Numerical simulations illustrate the effectiveness and feasibility of the proposed method.
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