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Robust impulsive synchronization of complex delayed dynamical networks. (English) Zbl 1221.34075

Summary: This Letter investigates robust impulsive synchronization of complex delayed dynamical networks with non-symmetrical coupling from the view of dynamics and control. Based on impulsive control theory on delayed dynamical systems, some simple yet generic criteria for robust impulsive synchronization are established. It is shown that these criteria can provide a novel and effective control approach to synchronize an arbitrary given delayed dynamical network to a desired synchronization state. Comparing with existing results, the advantage of the control scheme is that synchronization state can be selected as a weighted average of all the states in the network for the purpose of practical control strategy. Finally, numerical simulations are given to demonstrate the effectiveness of the proposed control methodology.

MSC:

34B45 Boundary value problems on graphs and networks for ordinary differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
34D06 Synchronization of solutions to ordinary differential equations
34C20 Transformation and reduction of ordinary differential equations and systems, normal forms
34H10 Chaos control for problems involving ordinary differential equations
60K20 Applications of Markov renewal processes (reliability, queueing networks, etc.)
93D21 Adaptive or robust stabilization
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