具有共存吸引子的混沌系统及其分数阶系统的镇定
Chaotic system with coexisting attractors and the stabilization of its fractional order system
摘要点击 78  全文点击 94  投稿时间:2017-12-20  修订日期:2018-07-03
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DOI编号  10.7641/CTA.2018.70943
  2019,36(2):262-270
中文关键词  混沌系统  分数阶系统  共存吸引子  拓扑马蹄  混沌控制
英文关键词  chaotic system  fractional order system  coexisting attractors  topological horseshoe  chaos control
基金项目  国家自然科学基金青年科学基金(批准号: 61602073)资助的课题.
学科分类代码  
作者单位E-mail
鲜永菊 重庆邮电大学 xianyj@cqupt.edu.cn 
夏诚 重庆邮电大学 s150101156@stu.cqupt.edu.cn 
钟德 重庆邮电大学  
徐昌彪 重庆邮电大学  
中文摘要
      研究一个具有共存吸引子的混沌系统及对应分数阶系统的镇定问题. 提出了一个新的具有双翼与四翼吸引子共存的混沌系统, 利用Lyapunov指数谱和分岔图等对系统的性质进行了分析. 找到了系统的拓扑马蹄和拓扑熵. 构造了相应的分数阶混沌系统, 此系统亦存在两个孤立的双翼吸引子以及四翼吸引子. 设计了线性反馈标量控制器, 此控制器用于分数阶混沌系统的镇定. 在控制过程中并未删除系统的非线性项, 理论分析与仿真计算表明了该方法的有效性.
英文摘要
      A chaotic system with coexistent attractors and the stabilization problem of the corresponding fractional order system are studied. A novel chaotic system with the existence of double-wing and four-wing chaotic attractors is proposed. Its math characteristics, Lyapunov exponents spectrum and bifurcation diagram are investigated, and the topological horseshoe and the topological entropy are obtained. Based on the system, a new 3D fractional order chaotic system is constructed. The fractional order system also has two isolated double-wing attractors and four-wing attractors, and there are not overlaps between the coexisting double wing attractors. For the stabilization of the fractional order system, a linear feedback scalar controller is designed. The nonlinear terms in the system are not deleted by the controlling method. The theoretical analysis and numerical simulation show the effectiveness of the method.