具有多种平衡点类型的大范围混沌系统及其拓扑马蹄

提出了一个新的三维混沌系统。通过调节系统中的参数,使系统在保持混沌动力学行为的同时分别具有多种类型的平衡点,即一个不稳定平衡点、无平衡点、无穷平衡点和一个稳定平衡点。此外,随着参数和初始值的变化,发现系统是一个大范围的混沌系统,且在无对称性条件下具有共存吸引子。分析了系统的基本动力学行为,包括系统的相图、Lyapunov指数谱和分岔图。利用拓扑马蹄理论和数值计算,找到了系统的拓扑马蹄,并获得拓扑熵,进一步从理论上证明系统的混沌特性。

A large range chaotic system with multiple types of equilibrium points and its topological horseshoe

A new three-dimensional chaotic system was proposed.By adjusting system parameters, the system may have multiple types of equilibrium points, such as an unstable equilibrium point, no equilibrium point, infinite equilibrium points and a stable equilibrium point, while maintaining its chaotic dynamical behaviors.In addition, with the change of parameters and initial values, it is found that the system is a large-scale chaotic system and has coexistence attractors under the condition of asymmetry.The system’s basic dynamic behaviors were analyzed by using the phase diagram, Lyapunov exponent spectrum and bifurcation diagram.By virtue of topological horseshoe theory and by means of numerical calculations, the system’s topological horseshoe and topological entropy were obtained, which further proves its chaotic characteristics in theory.