An active charge-controlled memristive Chua’s circuit is implemented, and its basic properties are analyzed. Firstly, with the system trajectory starting from an equilibrium point, the dynamic behavior of multiple coexisting attractors depending on the memristor initial value and the system parameter is studied, which shows the coexisting behaviors of point, period, chaos, and quasic-period. Secondly, with the system motion starting from a non-equilibrium point, the dynamics of extreme multistability in a wide initial value domain are easily conformed by new analytical methods. Furthermore, the simulation results indicate that some strange chaotic attractors like multi-wing type and multi-scroll type are observed when the observed signals are extended from voltage and current to power and energy, respectively. Specially, when different initial conditions are taken, the coexisting strange chaotic attractors between the power and energy signals are exhibited. Finally, the chaotic sequences of the new system are used for encrypting color image to protect image information security. The encryption performance is analyzed by statistic histogram, correlation, key spaces and key sensitivity. Simulation results show that the new memristive chaotic system has high security in color image encryption.

In this paper, the nonlinear dynamics of a Duffing nonautonomous oscillator with absolute function is investigated, and the switching boundary and the corresponding domains are shown. Based on the discontinuous dynamical theory, the motions of the non-smooth duffing system at the switching boundary are studied, and the corresponding analysis conditions of the different motions are obtained, and the parameter mappings are also given. Through numerical simulations, chaotic motions and period orbits are described in detail with different parameters and initial conditions, and the switching bifurcation diagrams through the boundary and basins of attractors are also drawn to investigate the behaviors of the system and coexistence of different attractors.

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