Synchronization of Discrete-Time Dynamical Networks with Time-Varying Couplings

We study the local complete synchronization of discrete-time dynamical networks with time-varying couplings. Our conditions for the temporal variation of the couplings are rather general and include variations in both the network structure and the reaction dynamics; the reactions could, for example, be driven by a random dynamical system. A basic tool is the concept of the Hajnal diameter, which we extend to infinite Jacobian matrix sequences. The Hajnal diameter can be used to verify synchronization, and we show that it is equivalent to other quantities which have been extended to time-varying cases, such as the projection radius, projection Lyapunov exponents, and transverse Lyapunov exponents. Furthermore, these results are used to investigate the synchronization problem in coupled map networks with time-varying topologies and possibly directed and weighted edges. In this case, the Hajnal diameter of the infinite coupling matrices can be used to measure the synchronizability of the network process. As ...

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