abstract

This paper proposes a new simple memristive chaotic system (MCS) containing an exponential term, a constant term, and a memristor-based nonlinear term. The system has dissipative feature and only one equilibrium. Its parameter-relied complex dynamics are comprehensive studied and the chaos with large parameter regions, multiple bifurcations, and large-scale amplitude modulation are revealed. The proposed system can realize the transition from stability to periodicity via Hopf bifurcation and generate chaos via period-doubling bifurcation with the increase or decrease of multiple parameters. The boundaries of chaotic attractors and the oscillation amplitudes of variables expand over a large-scale range as the parameter values continuously increase, indicating the emergence of large-scale amplitude modulation in the system. Moreover, the fixed-time synchronization (FxTS) problem is studied and the corresponding FxTS conditions are obtained by applying slide mode controller with the designed power reaching law. Both the theoretical derivation and numerical simulation consistently demonstrate the effectiveness of the obtained results.