摘要
吴，陈，和蔡(2007 ) 调查了一个线性州的错误反馈控制器单向性地联合的二个相同概括 Lorenz 系统的混乱同步。然而，在象复杂动态网络那样的真实生活的双向联合是更通用的。这份报纸为分析二个双向地联合的概括 Lorenz 系统的混乱同步提供一个统一方法。为联合矩阵的某专辑的一些足够的同步条件(斜矩阵，所谓的打乱的联合矩阵，等等) 通过严厉地数学的理论被导出。为古典 Lorenz 系统，特别地，作者获得仅仅用 Lorenz 系统的最终的界限的新评价取决于它的参数的同步标准(混乱， Solitons，和分数维图形， 2005 ) 。标准然后为确认在数字模拟被用于四个典型概括 Lorenz 系统。
Wu, Chen, and Cai （2007） investigated chaos synchronization of two identical generalized Lorenz systems unidirectionally coupled by a linear state error feedback controller. However, bidirec- tional coupling in real life such as complex dynamical networks is more universal. This paper provides a unified method for analyzing chaos synchronization of two bidirectionally coupled generalized Lorenz systems. Some sufficient synchronization conditions for some special coupling matrices （diagonal ma- trices, so-called dislocated coupling matrices, and so on） are derived through rigorously mathematical theory. In particular, for the classical Lorenz system, the authors obtain synchronization criteria which only depend upon its parameters using new estimation of the ultimate bounds of Lorenz system （Chaos, Solitons, and Fractals, 2005）. The criteria are then applied to four typical generalized Lorenz systems in the numerical simulations for verification.
基金
supported by the National Natural Science Foundation of China under Grant Nos.60804039 and 60974081
the National Basic Research Program of China under Grant No.2007CB310805
