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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2017, Vol. 34 ›› Issue (6): 591-598.doi: 10.3969/j.issn.1005-3085.2017.06.002

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地磁系统的混沌行为及其仿真与同步研究

王贺元,   阚   猛,   段文元   

  1. 辽宁工业大学理学院，锦州  121001
  • 收稿日期:2016-01-25 接受日期:2017-04-04 出版日期:2017-12-15 发布日期:2018-02-15
  • 基金资助:
    国家自然科学基金(11572146)；辽宁省教育厅科研基金(L2013248).

The Research and Simulation for Chaotic Behavior and Synchronization of the Earth's Magnetic Field System

WANG He-yuan,   KAN Meng,   DUAN Wen-yuan   

  1. College of Sciences, Liaoning University of Technology, Jinzhou 121001
  • Received:2016-01-25 Accepted:2017-04-04 Online:2017-12-15 Published:2018-02-15
  • Supported by:
    The National Natural Science Foundation of China (11572146); the Science Foundation of the Education Department of Liaoning Province (L2013248).

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摘要：

为了探讨磁流体动力学的本质特征，本文研究了地磁混沌系统的动力学行为及其数值仿真问题．文中求得了系统的定态，进行了线性稳定性分析，并对系统的混沌行为进行了数值仿真．仿真结果表明系统经亚临界霍普夫分岔到达混沌，混沌区内有周期窗口，当参数较大时系统最终形成环面．通过构造广义正定的Lyapunov函数，文中给出了地磁系统的全局吸引集和正向不变集，实现了系统全局指数同步，并对其进行计算机仿真，验证了该方法的有效性．

关键词: 地磁系统, 全局吸引集, 正向不变集, 全局指数同步

Abstract: In order to find the essential features of magnetohydrodynamics, this paper investigates the dynamical behavior and its synchronization of the earth's magnetic field system. We study the stability of stationary solutions to the earth's magnetic field system by using the linear stability analysis method. The chaotic behavior of the system is simulated, the simulation results show that the system can reach the chaos through the subcritical Hopf bifurcation, and there exists the periodic window in the chaotic region, a quasi-periodic regime could be formed at the high values of the parameter. The globally attractive set and positively invariant set of the earth's magnetic field system are discussed via constructing a generalized Lyapnov function. Further, an adaptive control approach is proposed to the synchronization between two chaotic systems. Numerical simulations show the effectiveness of the method.

Key words: earth's magnetic field system, global attractive set, positively invariant set, global exponential synchronization

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