一种具有多对称同质吸引子的四维混沌系统的超级多稳定性研究

该文在一个经典3维混沌系统的基础上提出一个新的具有超级多稳定性的4维混沌系统。新系统具有一个线平衡点，可以产生无限多对称的同质吸引子。通过相轨图和庞加莱截面等方法分析了系统的混沌特性。重点利用相轨图、分岔图和Lyapunov指数谱等方法分析了初始条件对系统超级多稳定性的影响，分析表明该系统具有很大的初值变化范围，除零点外恒定的Lyapunov指数谱，中心对称的离散分岔图。进一步地，该文研究了系统初值对称性与吸引子对称性的关系，不同于现有混沌系统中的对称吸引子，该系统可以产生无限多对称的同质吸引子。最后，利用电路仿真软件搭建模拟电路捕捉该系统的混沌吸引子，其结果验证了数值仿真的正确性。

Extreme Multi-stability of a Four-dimensional Chaotic System with Infinitely Many Symmetric Homogeneous Attractors

A new four-dimensional chaotic system with extreme multi-stability based on a classic three-dimensional chaotic system is proposed. The new system has a line equilibrium point, which can generate an infinite number of symmetrical homogeneous attractors. The chaotic characteristics of the system are analyzed by phase orbit diagram and Poincaré section methods. Using phase orbit diagrams, bifurcation diagrams and Lyapunov exponent spectrum methods, the influence of initial conditions on the extreme multi-stability of the system is analyzed. The analysis shows that the system has a large initial value variation range, and the Lyapunov exponent spectrum is constant except for the zero point. In addition, the system also has centrally symmetrical discrete bifurcation diagrams. Furthermore, the relationship between the initial symmetry of the system and the symmetry of the attractor is studied, which is different from the symmetrical attractor in the existing chaotic system, which can generate an infinite number of symmetrical homogeneous attractors. Finally, circuit simulation software is used to build an analog circuit to capture the chaotic attractor of the system, and the result verifies the correctness of the numerical simulation.