基于双曲正弦函数的四翼忆阻混沌系统及其FPGA实现

采用双曲正弦函数忆阻器作为正反馈项，设计了一个具有4个翅膀的四维混沌模型。首先利用四阶龙格库塔算法对该系统进行数值求解，对系统的稳定性进行了分析，发现系统只有一个平衡点且为鞍点。对系统进行动力学分析，绘制了随系统参数变化的Lyapunov指数和分岔图，计算了系统的Lyapunov维数，得到了系统随参数变化时运动状态的变化情况，发现系统存在周期和混沌等多种运动形态。最后，利用FPGA设计了一个混沌电路系统，用示波器观察结果，发现与数值结果基本一致，为忆阻混沌系统在通信中的应用奠定了基础。

A four-wing memristive chaotic system based on hyperbolic sine function and its FPGA implementation

Using the hyperbolic sine function memristor as the positive feedback term, a four- dimensional chaos model with four wings is designed. Firstly, the system is numerically solved using Runge-Kutta algorithm, and the stability of the system is analyzed. It is found that the system has only one equilibrium point as saddle point. Moreover, the dynamic analysis of the system is carried out, and the Lyapunov exponent and bifurcation diagram with the system parameters are drawn. Besides, the Lyapunov dimension of the system is calculated and the corresponding system is obtained. With the change of the motion states when the parameters change, it is found that there are many motion forms of the system, such as periods and chaos. Finally, a chaotic circuit system is designed by FPGA, and the results observed by oscilloscope are basically consistent with the numerical results, which lays a foundation for the application of memristor chaotic system in communication.