By introducing a memristor to the jerk system, a four-dimensional (4D) chaotic system is proposed. This system has five line equilibrium points with different stability. The extremely rich dynamic behaviors are studied by numerical simulation and theoretical analysis. Specifically, transient dynamics of coexisting chaotic attractors with different amplitudes at different time scales are found. And extreme multistability of mirror symmetric chaotic attractors, different scroll or amplitude of chaotic attractors, and different periodic attractors can be observed by selecting appropriate parameters and initial conditions. It is also found that the initial condition of the memristor can be used as the controller to realize the offset boost of the chaotic attractor. Then, the HSVII method, which includes state increment integral transformation and linear transformation, is used to reduce the dimension of the system and realize the transformation of correlation dynamics of initial condition into correlation dynamics of system parameter. It is proved numerically that the HSVII method is effective for the multistability analysis of the memristive chaotic system.

中文翻译：

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基于忆阻器的混沌系统中极其丰富的动力学

通过将忆阻器引入加加速度系统，提出了一种四维（4D）混沌系统。该系统具有五个具有不同稳定性的线路平衡点。通过数值模拟和理论分析研究了极其丰富的动力学行为。具体而言，发现了在不同时间尺度上具有不同幅度的共存混沌吸引子的瞬态动力学。通过选择适当的参数和初始条件，可以观察到镜面对称混沌吸引子的极度多重稳定性，混沌吸引子的不同涡旋或振幅以及不同周期的吸引子。还发现，忆阻器的初始状态可以用作控制器来实现混沌吸引子的偏置增强。然后，HSVII方法 它包括状态增量积分变换和线性变换，用于减小系统的尺寸，实现初始条件的相关动力学转换为系统参数的相关动力学。数值证明了HSVII方法对于忆阻混沌系统的多稳定性分析是有效的。