具有共存吸引子混沌系统的自适应同步控制  

Adaptive Synchronization Control of a Chaotic System with Coexisting Attractors

作　　者：颜闽秀 郭栋[1] YAN Minxiu;GUO Dong(School of Information Engineering,Shenyang University of Chemical Technology,Shenyang 110142,China;Key Laboratory of University of Liaoning Province for Collaborative Control and Optimization Technology of Industrial Environment-resources,Shenyang University of Chemical Technology,Shenyang 110142,China)

机构地区：[1]沈阳化工大学信息工程学院,辽宁沈阳110142 [2]沈阳化工大学工业环境-资源协同控制与优化技术辽宁省高校重点实验室,辽宁沈阳110142

出　　处：《控制工程》2024年第6期995-1003,共9页Control Engineering of China

基　　金：中国-北马其顿政府间科技合作项目(国科外[2019]22:6-8)。

摘　　要：在一个三维混沌系统的基础上,通过添加一个非线性反馈控制器,得到一个新的四维混沌系统。通过相图、功率谱、庞加莱截面、李雅普诺夫指数、平衡点等证明了系统的混沌特性,并通过分岔图分析了系统在不同参数下的运动状态。研究发现,该系统具有非常复杂的动力学行为和共存吸引子现象。同时,通过设置不同的初始值和不同的偏移增量,分别证明了系统具有共存吸引子,此结论对混沌保密通信等领域有一定的应用价值。通过0-1测试证明了混沌和周期运动的存在,并通过谱熵(spectral entropy,SE)算法和C0算法讨论了系统的复杂度。最后,设计了自适应同步控制器,仿真结果证明新系统可以在参数不确定的情况下实现同步控制,表明控制器是有效的。On the basis of a three-dimensional chaotic system,a new four-dimensional chaotic system is obtained by adding a nonlinear feedback controller.The chaotic properties of the system are proved by phase diagram,power spectrum,Poincarécross section,Lyapunov exponent,and equilibrium point.And the bifurcation diagram is used to analyze the motion state of the system under different parameters.It is found that the system has very complex dynamic behavior and coexisting attractor phenomenon.By setting different initial values and setting different offset increments,respectively.The existence of coexisting attractors is proved.It has certain application value in the fields of chaotic secure communication and so on.The existence of chaos and periodic motion is proved through 0-1 test,and the complexity of the system is discussed through spectral entropy(SE)algorithm and C0 algorithm.Finally,an adaptive synchronous controller is designed.The synchronous control is realized under certain conditions,which proves that the controller is effective.

关 键 词：混沌系统 复杂度分析 共存吸引子 自适应 同步控制 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]