In the present paper, synchronization and bifurcation of general complex dynamical networks are investigated. We mainly focus on networks with a somewhat general coupling matrix, i.e., the sum of each row equals a non...In the present paper, synchronization and bifurcation of general complex dynamical networks are investigated. We mainly focus on networks with a somewhat general coupling matrix, i.e., the sum of each row equals a nonzero constant u. We derive a result that the networks can reach a new synchronous state, which is not the asymptotic limit set determined by the node equation. At the synchronous state, the networks appear bifurcation if we regard the constant u as a bifurcation parameter. Numerical examples are given to illustrate our derived conclusions.展开更多
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...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.展开更多
基金The project supported by National Natural Science Foundation of China under Grant No, 70431002
文摘In the present paper, synchronization and bifurcation of general complex dynamical networks are investigated. We mainly focus on networks with a somewhat general coupling matrix, i.e., the sum of each row equals a nonzero constant u. We derive a result that the networks can reach a new synchronous state, which is not the asymptotic limit set determined by the node equation. At the synchronous state, the networks appear bifurcation if we regard the constant u as a bifurcation parameter. Numerical examples are given to illustrate our derived conclusions.
基金supported by the National Natural Science Foundation of China under Grant Nos.60804039 and 60974081the National Basic Research Program of China under Grant No.2007CB310805
文摘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.
