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Global synchronization in general complex delayed dynamical networks and its applications |
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| Authors: | Jin Zhou Lan Xiang |
| Institution: | a Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, PR China b Department of Physics, School of Science, Shanghai University, Shanghai 200444, PR China c Institute of System Biology, Shanghai University, Shanghai 200444, PR China |
| Abstract: | The main objective of the present paper is further to investigate global synchronization of a general model of complex delayed dynamical networks. Based on stability theory on delayed dynamical systems, some simple yet less conservative criteria for both delay-independent and delay-dependent global synchronization of the networks are derived analytically. It is shown that under some conditions, if the uncoupled dynamical node is stable itself, then the network can be globally synchronized for any coupling delays as long as the coupling strength is small enough. On the other hand, if each dynamical node of the network is chaotic, then global synchronization of the networks is heavily dependent on the effects of coupling delays in addition to the connection configuration. Furthermore, the results are applied to some typical small-world (SW) and scale-free (SF) complex networks composing of coupled dynamical nodes such as the cellular neural networks (CNNs) and the chaotic FHN neuron oscillators, and numerical simulations are given to verify and also visualize the theoretical results. |
| Keywords: | Complex dynamical networks Coupling time-delays Global synchronization Small-world networks Scale-free networks Cellular neural networks (CNNs) Chaotic FHN neuron oscillator |
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