He Wangli, Cao Jinde
Department of Mathematics, Southeast University, Nanjing, China.
Chaos. 2009 Mar;19(1):013118. doi: 10.1063/1.3076397.
In this paper, generalized synchronization of two chaotic systems is investigated. The auxiliary system approach, which is suggested by H. Abarbanel, N. Rulkov, and M. Sushchik [Phys. Rev. E 53, 4528 (1996)], is used to detect and study generalized synchronization. Based on the Lyapunov method and matrix measure, some less restrictive criteria are obtained to guarantee the asymptotical stability of the error system between the response system and the auxiliary system, which indicates the drive-response systems are synchronized in a general sense. It is shown that the feedback gain can be reduced by means of the matrix measure approach, compared to the norm method. All theoretical results are illustrated by analytical and numerical examples.
本文研究了两个混沌系统的广义同步。采用H. Abarbanel、N. Rulkov和M. Sushchik [《物理评论E》53, 4528 (1996)] 提出的辅助系统方法来检测和研究广义同步。基于李雅普诺夫方法和矩阵测度，得到了一些限制较少的准则，以保证响应系统与辅助系统之间误差系统的渐近稳定性，这表明驱动-响应系统在广义意义上是同步的。结果表明，与范数方法相比，通过矩阵测度方法可以降低反馈增益。所有理论结果都通过解析和数值例子进行了说明。
