摘要
本文讨论混沌连续时间系统的完全同步问题,提出一个构造混沌同步系统的新方法。这个方法基于线性系统的稳定性分析准则。通过对系统线性项与非线性项的适当分离,当系统的雅可比矩阵的所有特征值都具有负实部时,同步误差e(t)的线性系统是渐进稳定的,即可实现新系统和原系统的完全同步。新方法不需计算条件Lyapunov指数以作为判定同步的条件,因而比通用方法更为简单有效。新方法适用于自治或非自治系统,尤其适用于具有多于两个正Lyapunov指数的超混沌系统。甚至当初始同步误差极大时,也能实现理想的混沌同步。以Lorenz系统,耦合Duffing振子系统和超混沌R(?)ssler系统作为算例。数值计算结果证实所提出方法的有效性和鲁棒性。
The problem on the complete synchronization of a chaotic time-continuous systems was discussed, and a new approach for constructing chaotically synchronizing systems was proposed. This method was based upon the stability criterion of linear systems. Chaotic synchronization of time-continuous systems was achieved by means of appropriate separation of the chaotic system, when all eigenvalues of Jacobian matrix of the system have negative real parts which leads to that linear system of the synchronization error e(t) is asymptotically stable. Since the Lyapunov exponents are not required to calculate in construction of the new system, the proposed method is convenient for the synchronization of autonomous or non-autonomous systems, particularly for the synchronization of superchaotic systems with more than two positive Lyapunov exponents. The Lorenz system, the coupled Duffing oscillator and the R(?)ssler system were treated as numerical examples. The effectiveness and robustness of the new method is verified by the numerical results.
出处
《力学季刊》
CSCD
北大核心
2004年第1期9-14,共6页
Chinese Quarterly of Mechanics
基金
国家自然科学基金(10272074)
