忆阻超混沌Lü系统的隐藏动力学特性研究

通过改进经典Lü系统并引入忆阻元件，提出了一种新颖的基于忆阻的改进型Lü系统。该忆阻系统的最大特征是不存在任何平衡点，因此形成的动力学行为都是隐藏的。采用理论分析、李雅普诺夫指数和分岔图等非线性系统分析，研究了该忆阻系统随忆阻增益变化的周期、准周期、混沌和超混沌等复杂的隐藏动力学行为。此外，在初始条件不同时，该忆阻系统存在3个不同极限环以及混沌吸引子和周期极限环的共存多吸引子现象。制作硬件电路，验证了理论分析和数值仿真结果，表明了该忆阻超混沌Lü系统有着十分丰富而复杂的隐藏动力学特性。

Hidden Dynamical Characteristics in Memristor-Based Hyperchaotic Lü System

By improving the classical Lü system and introducing a generalized memristor, a novel memristor-based modified Lü system is proposed. The most important feature of this memristive system is that there does not exist any equilibrium point, thereby leading to that the forming dynamical behaviors are all hidden. By utilizing theoretical analyses and nonlinear system analysis methods of Lyapunov exponent spectrum and bifurcation diagram, the complex hidden dynamical behaviors, such as period, quasi-period, chaos, hyperchaos, and so on, with the variation of memristor gain for the memristive system are studied. In addition, when different initial conditions are used, the memristive system exhibits coexisting multiple attractors' phenomena of three different limit cycles as well as chaotic attractor and limit cycle. The hardware circuit is made and the experimental results verify the theoretical analysis and numerical simulations, and demonstrate that the proposed memristive Lü system has very abundant and complex hidden dynamical characteristics.