Adaptive and impulsive cluster synchronization of a general complex dynamical network

Recently, cluster synchronization has attracted an increasing interest in various disciplines, including mathematics, physics, and engineering sciences. This paper further investigates the cluster synchronization of a complex dynamical network by using adaptive and impulsive control techniques, respectively. Based on a complex dynamical network with two different clusters, several adaptive and impulsive cluster synchronization criteria are then proposed. It should be especially pointed out that the dynamics and its dimensions of the individual dynamical systems are different in the two different clusters. Also, some numerical simulations are given to verify the effectiveness of the above theoretical results.

[1]  Junan Lu.  Cluster Synchronization in a Complex Dynamical Network with Two Nonidentical Clusters , 2008, J. Syst. Sci. Complex..

[2]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[3]  Daizhan Cheng,et al.  Characterizing the synchronizability of small-world dynamical networks , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[4]  H. Cerdeira,et al.  Partial synchronization and spontaneous spatial ordering in coupled chaotic systems. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Guanrong Chen,et al.  Estimating the bounds for the Lorenz family of chaotic systems , 2005 .

[6]  Guanrong Chen,et al.  YET ANOTHER CHAOTIC ATTRACTOR , 1999 .

[7]  Guanrong Chen,et al.  A time-varying complex dynamical network model and its controlled synchronization criteria , 2005, IEEE Transactions on Automatic Control.

[8]  H. Haken,et al.  Detuned lasers and the complex Lorenz equations: Subcritical and supercritical Hopf bifurcations. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[9]  S. Strogatz.  Exploring complex networks , 2001, Nature.

[10]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[11]  Guanrong Chen,et al.  Chaos synchronization of general complex dynamical networks , 2004 .

[12]  Jinhu Lu,et al.  A New Chaotic Attractor Coined , 2002, Int. J. Bifurc. Chaos.

[13]  M. Hasler,et al.  Connection Graph Stability Method for Synchronized Coupled Chaotic Systems , 2004 .