Global synchronization of linearly hybrid coupled networks with time-varying delay. (English) Zbl 1161.94011

Summary: Many real-world large-scale complex networks demonstrate a surprising degree of synchronization. To unravel the underlying mechanics of synchronization in these complex networks, a generally linearly hybrid coupled network with time-varying delay is proposed, and its global synchronization is then further investigated. Several effective sufficient conditions of global synchronization are attained based on the Lyapunov function and a linear matrix inequality (LMI). Both delay-independent and delay-dependent conditions are deduced. In particular, the coupling matrix may be nonsymmetric or nondiagonal. Moreover, the derivative of the time-varying delay is extended to any given value. Finally, a small-world network, a regular network, and scale-free networks with network size are constructed to show the effectiveness of the proposed synchronous criteria.


94B50 Synchronization error-correcting codes
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34D20 Stability of solutions to ordinary differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
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