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
We propose a new modularity criterion in complex networks, called the unifying modularity q which is independent of the number of partitions. It is shown that, for a given network, the relationship between the upper l...We propose a new modularity criterion in complex networks, called the unifying modularity q which is independent of the number of partitions. It is shown that, for a given network, the relationship between the upper limit of Q and the number of the partitions, k, is sup（Qk） = （k - 1）/k. Since the range of Q for each partition number is inconsistent, we try to extend the concept Q to unifying modularity q, which is independent of the number of partitions. Subsequently, we indicate that it is more accurately to determine the number of partitions by using unifying modularity q than Q.展开更多
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 under Grant Nos 10832006 and 10802043, and Key Disciplines of Shanghai Municipality （S30104）.
文摘We propose a new modularity criterion in complex networks, called the unifying modularity q which is independent of the number of partitions. It is shown that, for a given network, the relationship between the upper limit of Q and the number of the partitions, k, is sup（Qk） = （k - 1）/k. Since the range of Q for each partition number is inconsistent, we try to extend the concept Q to unifying modularity q, which is independent of the number of partitions. Subsequently, we indicate that it is more accurately to determine the number of partitions by using unifying modularity q than Q.
