Synchronization for a class of complex dynamical networks with time-delay

Global asymptotical stability and generalized synchronization of phase synchronous dynamical networks

“…It is obvious that there are only diagonal matrices existing in (10), which ensures the validation of condition (6) in the theorem. From the stability of matrix A, it is straightforward to know that transfer functions…”

“…As people begin to consider the global synchronization problem for some special kinds of networks, the global synchronization for a class of dynamical complex networks composed of general Lur'e systems has been specifically investigated in virtue of the absolute stability theory [9,10]. Although the absolute stability has been extensively studied with the well-known circle and Popov criteria based on frequency-domain method and equivalent time-domain matrix inequality conditions, this kind of paradigm hardly lends itself to the analysis of nonlinear systems with multiple equilibria.…”

Exponential synchronization for arrays of coupled neural networks with time-delay couplings

“…Thus chaos synchronization for arrays of coupled DNNs have been discussed by the researchers, and many elegant results have been proposed in [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. In [7], by applying adaptive feedback controllers, the paper has studied the global synchronization of coupled complex networks with delayed coupling based on pinning control.…”

“…Yet, those above-mentioned results were presented via some kind of complicated inequalities, which makes them uneasily checked and applied to real ceases by the most recently developed algorithms. Though employing Lyapunov functional and Kronecker product, the global synchronization and cluster one have been studied for DNNs including robust ones and discrete-time ones with delayed coupling or one single delayed coupling via LMIs in [13][14][15][16][17][18][19][20][21], and some easy-to-test sufficient conditions have been obtained. Yet, the system forms in [13][14][15][16][17][18][19][20][21] seemed simple and the most improved techniques in [22,23] weren't utilized to achieve the criteria, which make these results inapplicable to deal with DNNs of more general forms.…”

“…Recently, the problem on synchronization has been extensively investigated in chaotic systems owing to the potential applications in various engineering areas. Especially, since chaos synchronization in arrays of linearly coupled dynamical systems was firstly considered by [3], arrays of coupled systems including coupled delayed chaotic ones have attracted the researchers' attention as they can exhibit some interesting phenomena [4,5], and many elegant results have been derived in [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21].…”