Showing papers by "Xiwei Liu published in 2007"
TL;DR: In this paper, a single controller can pin a coupled complex network to a homogeneous solution, and sufficient conditions are presented to guarantee the convergence of the pinning process locally and globally.
Abstract: In this paper, without assuming symmetry, irreducibility, or linearity of the couplings, we prove that a single controller can pin a coupled complex network to a homogenous solution. Sufficient conditions are presented to guarantee the convergence of the pinning process locally and globally. An effective approach to adapt the coupling strength is proposed. Several numerical simulations are given to verify our theoretical analysis.
945 citations
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TL;DR: It is proved that a single controller can pin a coupled complex network to a homogenous solution without assuming symmetry, irreducibility, or linearity of the couplings.
Abstract: In this paper, without assuming symmetry, irreducibility, or linearity of the couplings, we prove that a single controller can pin a coupled complex network to a homogenous solution. Sufficient conditions are presented to guarantee the convergence of the pinning process locally and globally. An effective approach to adapt the coupling strength is proposed. Several numerical simulations are given to verify our theoretical analysis.
837 citations
TL;DR: Sufficient conditions for both delay-independent and delay-dependent global exponential synchronization are obtained based on Lyapunov functional method and it is shown that, for some coupled chaotic systems and nonlinear coupling functions, if the coupling delay is less than a positive threshold, then the coupled network will be synchronized.
Abstract: In this paper, we discuss exponential synchronization of nonlinear coupled dynamical networks with a delayed coupling. Sufficient conditions for both delay-independent and delay-dependent global exponential synchronization are obtained based on Lyapunov functional method. It is shown that, for some coupled chaotic systems and nonlinear coupling functions, if the coupling delay is less than a positive threshold, then the coupled network will be synchronized. On the other hand, with the increase of coupling delay, the synchronizability of the coupled network will be restrained, even eventually de-synchronized. Finally, an example is provided to demonstrate the effectiveness of the proposed results.
92 citations