We investigate the collective dynamics of network-organized identical excitable nodes. We theoretically analyze the stability of the rest state and propose that there are two different transition paths： the stationar...We investigate the collective dynamics of network-organized identical excitable nodes. We theoretically analyze the stability of the rest state and propose that there are two different transition paths： the stationary path and the oscillatory path. We find that, although the onset of collective dynamics strongly depend on the network topology, the local dynamics and how local nodes interact with each other decide the transition path and the involved bifurcation.展开更多
Cluster synchronization is an important dynamical behavior in community networks and deserves further investigations.A community network with distributed time delays is investigated in this paper.For achieving cluster...Cluster synchronization is an important dynamical behavior in community networks and deserves further investigations.A community network with distributed time delays is investigated in this paper.For achieving cluster synchronization,an impulsive control scheme is introduced to design proper controllers and an adaptive strategy is adopted to make the impulsive controllers unified for different networks.Through taking advantage of the linear matrix inequality technique and constructing Lyapunov functions,some synchronization criteria with respect to the impulsive gains,instants,and system parameters without adaptive strategy are obtained and generalized to the adaptive case.Finally,numerical examples are presented to demonstrate the effectiveness of the theoretical results.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No 71301012
文摘We investigate the collective dynamics of network-organized identical excitable nodes. We theoretically analyze the stability of the rest state and propose that there are two different transition paths： the stationary path and the oscillatory path. We find that, although the onset of collective dynamics strongly depend on the network topology, the local dynamics and how local nodes interact with each other decide the transition path and the involved bifurcation.
基金Project supported by the National Natural Science Foundation of China(Grant No.61463022)the Natural Science Foundation of Jiangxi Province,China(Grant No.20161BAB201021)the Natural Science Foundation of Jiangxi Educational Committee,China(Grant No.GJJ14273)
文摘Cluster synchronization is an important dynamical behavior in community networks and deserves further investigations.A community network with distributed time delays is investigated in this paper.For achieving cluster synchronization,an impulsive control scheme is introduced to design proper controllers and an adaptive strategy is adopted to make the impulsive controllers unified for different networks.Through taking advantage of the linear matrix inequality technique and constructing Lyapunov functions,some synchronization criteria with respect to the impulsive gains,instants,and system parameters without adaptive strategy are obtained and generalized to the adaptive case.Finally,numerical examples are presented to demonstrate the effectiveness of the theoretical results.
