新混沌系统的动力学分析  

Dynamical Analysis of New Chaotic System

作　　者：张转周 刘衍民 秦进 ZHANG Zhuan-zhou, LIU Yan-min, QIN Jin(College of Mathematics, Zunyi Normal University, Zunyi 563006, Chin)

机构地区：[1]遵义师范学院数学学院

出　　处：《数学的实践与认识》2018年第14期256-261,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(71461027,71471158);贵州省科学技术基金项目(黔科合LH字[2015]7005号);贵州省教育厅青年科技人才成长项目(黔教合KY字[2017]256);贵州省自然科学基金(黔教合KY[2014]295);遵义市创新人才团队(遵市科合(2015)38号);遵义师范学院教研项目(15-29)基金资助项目;贵州省科技合作项目(黔科LH字[2015]7042号)

摘　　要：基于动力系统的理论和方法，构造出一个具有复杂混沌吸引子的非线性混沌自治三维系统．其与经典的混沌系统具有类似的结构与性态．采用理论分析和Matlab仿真相结合的方式研究，得到了系统在平衡点处不稳定的参数范围．通过分岔图和Lyapunov指数谱进一步揭示了系统丰富的动力学行为，Matlab模拟验证了计算理论的正确性．This research is undertaken to build a three-dimensional autonomous chaotic nonlinear system with complex chaotic attractors based on the theory and method of dynamical system, which is similar to the classical chaotic system in structure and behavior. The uastable range of parameters at the equilibrium point of the system is detected through theoretical analysis and Matlab simulation. The research further unfolds many dynamical behaviors of the system by bifurcation diagram and Lyapunov exponent spectrum. The theoretical calculation has been proved correct through Matlab simulation.

关 键 词：混沌系统 稳定性 分岔 LYAPUNOV指数 

分 类 号：O415.5[理学—理论物理]