不同空间Julia集的非线性广义同步(英文)
Nonlinear generalized synchronization of two different spatial Julia sets
摘要点击 1981  全文点击 1451  投稿时间:2012-05-04  修订日期:2013-05-31
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DOI编号  10.7641/CTA.2013.12095
  2013,30(9):1159-1164
中文关键词  空间Julia集  广义同步  稳定区域  复杂的
英文关键词  spatial Julia sets  generalized synchronization  stable domain  complex
基金项目  This work was supported by the National Natural Science Foundation of China (Nos. 60874009 and 10971120), and the Natural Science Foundation of Shandong province (No. ZR2010FM010).
作者单位E-mail
刘平 山东农业大学 机械与电子工程学院
山东省园艺机械与装备重点实验室
山东大学 控制科学与工程学院 
pingliu@mail.sdu.edu.cn 
刘树堂 山东大学 控制科学与工程学院  
中文摘要
      基于利用线性耦合实现空间Julia 集线性广义同步的研究成果, 本文通过应用非线性反馈控制和引入变量变换的方法解决了空间Julia集的非线性广义同步问题. 首先基于变量变换, 得到误差空间Julia系统, 为了镇定该系统使其实现非线性广义同步, 给出了确定的非线性函数关系式. 另外, 根据空间Julia集的稳定区域, 解析地确定了实现非线性广义同步的耦合强度的稳定域. 然后, 给出了稳定的复不动平面与空间Julia集的同步的关系. 最后, 用一个例子验证了该解析方法是可行的.
英文摘要
      Referring to the realization of linear generalized synchronization for spatial Julia sets using linear coupling, we deal with its nonlinear generalized synchronization by applying nonlinear feedback control and introducing a multivariable transform in this work. Based on this multi-variable transform, the error spatial Julia system is obtained and the nonlinear function is given to stabilize the error spatial Julia system such that the generalized synchronization will be achieved. Moreover, according to the stability domains given for spatial Julia sets, we determine analytically the stability domain of the coupling strength for the generalized synchronization. Then, the relationship between the complex stable fixed plane and the synchronization of the spatial Julia sets is also analyzed. Finally, an example is presented to validate the scheme and the analysis.