Theoretical analysis of synchronization in delayed complex dynamical networks with discontinuous coupling

Abstract

In this paper, we study the synchronization problem of time-delayed complex networks with discontinuous coupling. Sufficient conditions for the synchronization are obtained based on the stability theory of differential equations. The theoretical results show that the time-delayed networks can achieve synchronization even if the coupling is switched off sometimes. We find analytically that the speed of synchronization is proportional to the on-off rate of the coupling and the algebraic connectivity of networks. Finally, the analytical results are confirmed by numerical simulations.

Finite-time synchronization of uncertain complex dynamic networks with time-varying delay

“…The fractional-order synchronization of complex network systems subjected to coupling delay was investigated [10]. Sun et al [11] theoretically analyzed the feasibility of a complex dynamic network with time delay and discontinuous internal coupling relationship to achieve synchronization. Ma et al [12] proposed several sufficient conditions that can facilitate synchronization of a single complex network with Markovian jump and time-varying delay by using a pinning control strategy.…”

Synchronization of Complex Dynamical Networks with Dynamical Behavior Links

“…The problem of delayed couplings, with its strong analytical background and its definitive existence in many real systems due to the limited speed of data transmission, has been extensively studied [5,21,22]. Xu [24]. In a practical point of view, the links exhibit dynamic behavior, especially for biological networks and for complex dynamical networks in which electrical wires are utilized as links.…”

“…have considered mixed non‐derivative and derivative linear couplings , while Sun et al. have proposed discontinuous couplings . In a practical point of view, the links exhibit dynamic behavior, especially for biological networks and for complex dynamical networks in which electrical wires are utilized as links.…”