| 摘要: |
| 针对3D Lorenz型系统，提出了具有唯一平衡点或两个平衡点的四维超混沌系统, 在两种不同平衡点情形下可分别发现超混沌吸引子。通过构造恰当的Lyapunov函数严格证明同宿轨与异宿轨的不存在性, 表明此系统的超混沌是非Shil’nikov意义下的混沌；进一步将Lyapunov函数和优化方法有机结合证明超混沌吸引子的最终有界性，并数值模拟验证超混沌吸引子的最终有界；运用相图、Lyapunov指数谱、分岔图和Poincaré映射分析系统随参数变化的复杂动力学。 |
| 关键词: 超混沌 混沌 同宿轨 异宿轨 最终有界 |
| DOI： |
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| Ultimate Boundedness of a Non Shil’nikov Type 4D Hyperchaotic System |
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NIU Ya-xing, YANG Qi-gui
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chool of Mathematics, South China University of Technology, Guangzhou 510640, China
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| Abstract: |
| We report a novel four dimensional (4D) hyperchaotic system with a unique equilibrium or two equilibria based on 3D Lorenz type system,and can clearly observe hyperchaotic attractors at each type of equilibria. By utilizing proper Lyapunov function and analytical method,we rigorously prove the nonexistence of homoclinic orbit and heteclinic orbit, further, the hyperchaos of system is no chaos in the sense of Shil’nikov. Further, the ultimate bound sets of system are constructed by Lyapunov function and appropriate optimization. Moreover, the results are verified by numerical simulation method. The complex dynamics are exhibited with the changing parameter by phase portrait, Lyapunov exponents spectrum,bifurcation diagram and Poincare mapping analysis system. |
| Key words: hyperchaos chaos homoclinic orbit heteclinic orbit ultimate bound |
