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Average contraction and synchronization of complex switched networks. (English) Zbl 1262.34059

Author’s abstract: The paper introduces an average contraction analysis for nonlinear switched systems and applies it to investigate the synchronization of complex networks of coupled systems with switching topology. For a general nonlinear system with time-dependent switching law, a basic convergence result is presented according to the average contraction analysis, and a special case, where the trajectories of a distributed switched system converge to a linear subspace is then investigated. Synchronization is viewed as the special case with all trajectories approaching the synchronization manifold, and is thus studied for complex networks of coupled oscillators with switching topology. It is shown that the synchronization of a complex switched network can be evaluated by the dynamics of an isolated node, the coupling strength and the time average of the smallest eigenvalue associated with the Laplacians of switching topology and the coupling fashion. Finally, numerical simulations illustrate the effectiveness of the proposed methods.

MSC:

34D06 Synchronization of solutions to ordinary differential equations
34A36 Discontinuous ordinary differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
34C29 Averaging method for ordinary differential equations
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