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

Yu, Wenwu; Cao, Jinde; Lü, Jinhu

SIAM J. Appl. Dyn. Syst. 7, No. 1, 108-133 (2008).

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.

MSC:

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

Keywords:

Lyapunov function; linear matrix inequality (LMI); global synchronization; time-varying delay; complex networks