一类非Shil’nikov型四维超混沌系统的最终有界  

Ultimate Boundedness of a Non-Shil’nikov Type 4D Hyperchaotic System

作　　者：牛亚星 杨启贵 NIU Ya-xing;YANG Qi-gui(School of Mathematics,South China University of Technology,Guangzhou 510640,China)

机构地区：[1]华南理工大学数学学院,广州510640

出　　处：《重庆工商大学学报（自然科学版）》2020年第4期20-27,共8页Journal of Chongqing Technology and Business University:Natural Science Edition

基　　金：国家自然科学基金项目资助(11671149).

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。We report a novel four-dimensional(4 D)hyperchaotic system with a unique equilibrium or two equilibria based on 3 D 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.

关 键 词：超混沌 混沌 同宿轨 异宿轨 最终有界 

分 类 号：O127[理学—数学]