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.
Bidirectionally-coupled chaos generalized lorenz system synchronization ultimate bound
This is a preview of subscription content, log in to check access.
J. Zhou, J. Lu, and X. Wu, Linearly and nonlinearly bidirectionally coupled synchronization of hyperchaotic systems, Chaos, Solitons and Fractals, 2007, 31: 230–235.MathSciNetzbMATHCrossRefGoogle Scholar
X. Wu, G. Chen, and J. Cai, Chao synchronization of the master-slave generalized Lorenz systems via linear state error feedback control, Physica D, 2007, 229: 52–80.MathSciNetzbMATHCrossRefGoogle Scholar
L. Chen and J. Lu, Cluster synchronization in a complex dynamical network with two nonidentical clusters, Journal Systems Science & Complexity, 2008, 21(1): 20–33.MathSciNetzbMATHCrossRefGoogle Scholar