Cluster synchronization in a network of non-identical dynamic systems is studied in this paper, using two-cluster synchronization for detailed analysis and discussion. The results show that the common intercluster cou...Cluster synchronization in a network of non-identical dynamic systems is studied in this paper, using two-cluster synchronization for detailed analysis and discussion. The results show that the common intercluster coupling condition is not always needed for the diffusively coupled network. Several sufficient conditions are obtained by using the Schur unitary triangularization theorem, which extends previous results. Some numerical examples are presented for illustration.展开更多
Cluster synchronization of nonlinear uncertain complex networks with desynchronizing impulse is explored. First of all, a feedback controller is employed, based on the Lyapunov stability theorem and Lipschitz conditio...Cluster synchronization of nonlinear uncertain complex networks with desynchronizing impulse is explored. First of all, a feedback controller is employed, based on the Lyapunov stability theorem and Lipschitz condition, to guarantee that the uncertain complex networks with desynchronizing impulse synchronize with an object trajectory. Furthermore, a synchronizing impulse controller is presented, which is more efficiently and directly used to achieve the cluster synchronization. Finally, numerical examples are examined to show the effectiveness of the proposed methods.展开更多
This paper deals with the cluster exponential synchronization of a class ot complex networks wlm nyorm coupm^g and time-varying delay. Through constructing an appropriate Lyapunov-Krasovskii functional and applying th...This paper deals with the cluster exponential synchronization of a class ot complex networks wlm nyorm coupm^g and time-varying delay. Through constructing an appropriate Lyapunov-Krasovskii functional and applying the theory of the Kronecker product of matrices and the linear matrix inequality （LMI） technique, several novel sufficient conditions for cluster exponential synchronization are obtained. These cluster exponential synchronization conditions adopt the bounds of both time delay and its derivative, which are less conservative. Finally, the numerical simulations are performed to show the effectiveness of the theoretical results.展开更多
In this paper, cluster synchronization in community network with nonidentical nodes is investigated. By combining intermittency with a pinning control scheme, some effective controllers are designed. In the control sc...In this paper, cluster synchronization in community network with nonidentical nodes is investigated. By combining intermittency with a pinning control scheme, some effective controllers are designed. In the control scheme, only one node in each community is controlled and coupling weights of a spanning tree in each community are enhanced. Based on the Lyapunov function method and mathematical analysis technique, two results for achieving cluster synchronization are obtained. Noticeably, by introducing an adaptive strategy, some universal adaptive intermittent pinning controllers are designed for different networks. Finally, two numerical simulations are performed to verify the correctness of the derived results.展开更多
We investigate a new cluster projective synchronization （CPS） scheme in time-varying delay coupled complex dynamical networks with nonidentical nodes. Based on the community structure of the networks, the controller...We investigate a new cluster projective synchronization （CPS） scheme in time-varying delay coupled complex dynamical networks with nonidentical nodes. Based on the community structure of the networks, the controllers are designed differently for the nodes in one community, which have direct connections to the nodes in the other communities and the nodes without direct connections to the nodes in the other communities. Some sufficient criteria are derived to ensure the nodes in the same group projectively synchronize and there is also projective synchronization between nodes in different groups. Particularly, the weight configuration matrix is not assumed to be symmetric or irreducible. The numerical simulations are performed to verify the effectiveness of the theoretical results.展开更多
基金Project supported by the "13115" Program, China (Grant No. 2008ZDKG-37)the National Natural Science Foundation of China (Grant Nos. 61072139, 61072106, 60804021, and 61001202)the Fundamental Research Funds for the Central Universities of China (Grant Nos. Y10000902036, JY10000902039, JY10000970001, and JY10000902001)
文摘Cluster synchronization in a network of non-identical dynamic systems is studied in this paper, using two-cluster synchronization for detailed analysis and discussion. The results show that the common intercluster coupling condition is not always needed for the diffusively coupled network. Several sufficient conditions are obtained by using the Schur unitary triangularization theorem, which extends previous results. Some numerical examples are presented for illustration.
基金Project supported by the National Natural Science foundation of China(Grant Nos.51276081 and 11326193)the Students’ Research Foundation of Jiangsu University,China(Grant Nos.Y13A127 and 12A415)
文摘Cluster synchronization of nonlinear uncertain complex networks with desynchronizing impulse is explored. First of all, a feedback controller is employed, based on the Lyapunov stability theorem and Lipschitz condition, to guarantee that the uncertain complex networks with desynchronizing impulse synchronize with an object trajectory. Furthermore, a synchronizing impulse controller is presented, which is more efficiently and directly used to achieve the cluster synchronization. Finally, numerical examples are examined to show the effectiveness of the proposed methods.
基金supported by the National Natural Science Foundation of China (Grant Nos. 61074073 and 61034005)the Fundamental Research Funds for the Central Universities of China (Grant No. N110504001)the Open Project of the State Key Laboratory of Management and Control for Complex Systems, China (Grant No. 20110107)
文摘This paper deals with the cluster exponential synchronization of a class ot complex networks wlm nyorm coupm^g and time-varying delay. Through constructing an appropriate Lyapunov-Krasovskii functional and applying the theory of the Kronecker product of matrices and the linear matrix inequality （LMI） technique, several novel sufficient conditions for cluster exponential synchronization are obtained. These cluster exponential synchronization conditions adopt the bounds of both time delay and its derivative, which are less conservative. Finally, the numerical simulations are performed to show the effectiveness of the theoretical results.
基金Project supported jointly by the National Natural Science Foundation of China(Grant No.61463022)the Natural Science Foundation of Jiangxi Province of China(Grant No.20132BAB201016)+1 种基金the Natural Science Foundation of Jiangxi Educational Committee,Jiangxi Province,China(Grant No.GJJ14273)the Graduate Innovation Fund of Jiangxi Normal University(Grant No.YJS2014061)
文摘In this paper, cluster synchronization in community network with nonidentical nodes is investigated. By combining intermittency with a pinning control scheme, some effective controllers are designed. In the control scheme, only one node in each community is controlled and coupling weights of a spanning tree in each community are enhanced. Based on the Lyapunov function method and mathematical analysis technique, two results for achieving cluster synchronization are obtained. Noticeably, by introducing an adaptive strategy, some universal adaptive intermittent pinning controllers are designed for different networks. Finally, two numerical simulations are performed to verify the correctness of the derived results.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 70871056 and 71271103)the Six Talents Peak Foundation of Jiangsu Province,China
文摘We investigate a new cluster projective synchronization （CPS） scheme in time-varying delay coupled complex dynamical networks with nonidentical nodes. Based on the community structure of the networks, the controllers are designed differently for the nodes in one community, which have direct connections to the nodes in the other communities and the nodes without direct connections to the nodes in the other communities. Some sufficient criteria are derived to ensure the nodes in the same group projectively synchronize and there is also projective synchronization between nodes in different groups. Particularly, the weight configuration matrix is not assumed to be symmetric or irreducible. The numerical simulations are performed to verify the effectiveness of the theoretical results.
