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Pure Mathematics 2020
一个有任意给定数目平衡点的四维超混沌系统
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Abstract:
本文介绍了一种基于分段盘式发电机系统的四维超混沌ODE系统。当参数变化时，该系统可以有任意给定数量的平衡点。本文给出了该系统的许多有趣的混沌性质：(i) 没有平衡点的系统存在隐藏混沌吸引子；(ii) 具有两个非双曲平衡点的系统存在超混沌吸引子；(iii) 具有六个不稳定平衡点的系统存在混沌吸引子；(iv) 具有无穷多个不稳定孤立平衡点的系统存在无穷多个混沌吸引子；(v) 具有线平衡点的系统存在混沌吸引子。本文进一步证明了在适当的参数条件下，系统在两个平衡点上同时发生Hopf分叉。数值模拟证明了Hopf分叉的存在。
This paper introduces a 4D hyperchaotic ODE system based on segmented disc dynamo system. The system can have any given number of equilibrium when parameters vary. Many interesting chaotic properties of the system are also given: (i) a hidden chaotic attractor exists with no equilibria; (ii) a hyperchaotic attractor exists with two non-hyperbolic equilibria; (iii) a chaotic attractor exists with six unstable equilibria; (iv) chaotic attractors coexist with infinitely many unstable isolated equilibria; (v) a chaotic attractor exists with line equilibrium. The paper further proves that Hopf bifurcation occurs simultaneously at two equilibria in the system under appropriate parameter conditions. Numerical simulation demonstrates the emergence of the Hopf bifurcation.
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