Journal of Systems Science and Complexity

, Volume 24, Issue 3, pp 433–448 | Cite as

Bidirectionally coupled synchronization of the generalized Lorenz systems

  • Juan ChenEmail author
  • Jun-an Lu
  • Xiaoqun Wu


Wu, Chen, and Cai (2007) investigated chaos synchronization of two identical generalized Lorenz systems unidirectionally coupled by a linear state error feedback controller. However, bidirectional 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 matrices, 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.

Key words

Bidirectionally-coupled chaos generalized lorenz system synchronization ultimate bound 


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Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsWuhan UniversityWuhanChina

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