Synchronization Of Complex Dynamical Networks Based On Impulsive Control

Synchronization of complex dynamical network has been a hot topic in many fields because of its widely applications in the real world. More and more researchers focus on impulsive control as a typical discontinuous control method.for its low cost, high efficiency, easy to implement, simple structure, Bases on impulsive control, this paper apply the method of Lyapunov functions to study the synchronization of complex-variable chaotic system and dynamic network and parameter identification.Firstly, based on impulsive stability theory for impulsive system, synchronization of drive-response complex-variable chaotic systems is investigated, adaptive strategy is adopted to relax the restriction on the impulsive interval, impulsive gain can change adaptively, then one can have more universality and efficient synchronization criteria. Meanwhile, the uncertain system parameters can be identify, numerical simulations are given to verify the effectiveness of the derived results.Secondly, impulsive synchronization of dynamic network coupling with different complex-variable chaotic systems is investigated, the problem of network with uncertain topological struc-ture and both uncertain topological structure and system parameters are considered. Base on impulsive stability theory, under the assumption of linearly independence, adopted adaptive strat-egy, then one can get synchronization criteria of the network. In addition, this method can be appropriate for uncertain complex-variable dynamical networks with different node dynamics and also can deliver online monitoring, several different networks in numerical simulations are given to demonstrate the effectiveness of the theoretical results.Finally, pinning impulsive synchronization of complex-variable dynamical networks coupled with complex-variable chaotic system, Based on Lyapunov stability theory for impulsive system, an efficient strategy is proposed to choose the suitable pinning nodes to be impulsive controlled, in general, these nodes could be different at impulsive time instants. Furthermore, the adaptive strategy is adopt to relax the restriction on the impulsive intervals. Numerical example is provided to show the effectiveness of the proposed method.