| 摘要: |
| 针对仅有一个平衡点的非线性超混沌系统能否产生多卷吸引子这一问题，提出了仅包含一个非线性项且具有唯一平衡点的新四维多卷超混沌光滑系统；基于Sprott构造的三维Jerk混沌系统，结合反馈控制技术及多卷混沌系统的设计方法，利用Routh-Hurwitz判别准则、中心流形定理以及数学仿真软件，对新系统的复杂动力学性质进行了深入地理论分析和探讨；研究发现系统存在唯一的平衡点，且给出此平衡点在不同状态下的参数适用范围，严格证明了新系统存在Hopf分岔现象，进一步数值模拟获得新系统的Lyapunov指数谱、分岔图和Poincaré映射等特征，验证了新系统仅有一个鞍-焦点且能够产生多卷超混沌吸引子、周期吸引子等复杂的动力学行为，丰富了现有Jerk系统的超混沌复杂性研究。 |
| 关键词: 超混沌系统 多卷系统 Jerk系统 Lyapunov指数 Hopf分岔 |
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| Research on Complex Dynamics of a New 4D Multi-scroll |
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HAN Jie, YANG Qi-gui
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School of Mathematics, South China University of Technology, Guangzhou 510640, China
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| Abstract: |
| To solve the problem whether a nonlinear hyperchaotic system with only one equilibrium point can generate multi-scroll attractors, a new 4D hyperchaotic smooth system with one nonlinear term and a unique equilibrium point is proposed. Based on the 3D Jerk chaotic system constructed by Sprott, the complex dynamic properties of the new system are analyzed and discussed theoretically by using the Routh-Hurwitz criterion, the central manifold theorem and the mathematical simulation software, and by combining with the feedback control technology and the design method of multi-scroll chaotic system. It is found that there is a unique equilibrium point in the system, and the applicable parameters range of this equilibrium point in different states is given. It is strictly proved that the Hopf bifurcation phenomenon exists in the new system, and the Lyapunov exponential spectrum, bifurcation graph and Poincaré mapping of the new system are further obtained by numerical simulation. It is verified that the new system has only one saddle-focus and can produce complex dynamics such as multi-scroll hyperchaotic attractor and periodic attractor, which enriches the research on hyperchaotic complexity of the existing Jerk system. |
| Key words: hyperchaotic system multi-scroll system Jerk system Lyapunov exponents Hopf bifurcation |
