Generalized Lag Synchronization of Multiple Weighted Complex Networks with Fixed and Adaptive Couplings

The generalized lag synchronization for multi-weighted complex dynamical network with fixed and adaptive couplings is investigated in this paper, respectively. By designing appropriate controller, a synchronization criterion is presented for complex dynamical network with multi-weights based on the selected Lyapunov functional and inequality techniques. Moreover, an adaptive scheme to update the coupling weights is also developed for ensuring the generalized lag synchronization of multi-weighted complex dynamical network. Finally, two examples are given to validate effectiveness of the proposed generalized lag synchronization criteria.

1 Introduction

Recently, the dynamical behaviors of complex networks have been widely investigated. In particular, lots of researchers have discussed the synchronization problem for complex networks, and many important results have been presented [1]–[3]. In[1], Feng et al. considered the stochastic synchronization of coupled neural networks based on Kronecker product and Lyapunov functional method. Wang et al. [2] studied the synchronization for a coupled reaction-diffusion neural networks by utilizing the output strict passivity. In [3], Lu et al. proposed some criteria for ensuring the synchronization by designing appropriate pinning controllers.