Delayed impulsive synchronization of discrete-time complex networks with distributed delays

Abstract

In this paper, a novel delayed impulsive control strategy is proposed for synchronization of discrete-time complex networks with distributed delays. Different from the existing results, the involving time delays include distributed delays and impulsive input delays. Employing the Razumikhin theorem and the mathematical induction method, several sufficient criteria are derived in terms of algebraic conditions, which depend on impulsive input delays and impulsive control gains. Meanwhile, the derived criteria also reveal the relationship between the bounds of impulsive intervals and impulsive input delays. Finally, two examples are given to illustrate the effectiveness of the proposed approach.

Synchronization of delayed neural networks with hybrid coupling via impulsive control

“…During the 1970s, some authors pointed out that the use of distributed-delays in biology can lead the models to be more tractable and more realistic than those with discrete-delays (MacDonald, 1980). It is thus necessary and important to study the synchronization problem of the coupled neural networks with distributed-delay coupling (Cao et al, 2008; He et al, 2017; Hu et al, 2014; Leng and Wu, 2016; Li et al, 2015; Yuan, 2009). Several dynamical properties of the neural networks with distributed-delay were investigated, such as passivity analysis (Wen et al, 2015; Yu and Cao, 2018), stability (Liu et al, 2006) and almost periodic solution (Jiang et al, 2015).…”

“…Several dynamical properties of the neural networks with distributed-delay were investigated, such as passivity analysis (Wen et al, 2015; Yu and Cao, 2018), stability (Liu et al, 2006) and almost periodic solution (Jiang et al, 2015). In addition, the delayed impulsive control (Li et al, 2015) was used to study the synchronization of the discrete CDNs with distributed-delays, and the results dependent on the impulsive control delay has been obtained in terms of algebraic inequality. The novel pinning strategy (He et al, 2017) was proposed to obtain the synchronization of the coupled neural networks with two different connected topologies, that is, the delay-free connected topology and the distributed-delay connected topology.…”

“…Motivated by the above discussion, the synchronization criteria dependent on both distributed-delay and transmission delay are investigated for the coupled neural networks with distributed-delay coupling in the present paper. The nodes of the studied coupled neural networks are nonidentical, rather than the identical nodes (Cao et al, 2008; He et al, 2017; Li et al, 2015; Yuan, 2009). The object is to design a hybrid control to completely synchronize the coupled delayed neural networks.…”

Exponential Synchronization of Dynamical Network with Distributed Delays Via Intermittent Control

“…That is, this class of delayed systems cannot be modelled by dynamical networks without or with coupling delays (constant or time-varying delays). Naturally, dynamical networks with distributed delays are presented to describe the above systems and widely studied [31][32][33][34][35][36][37][38]. In Refs.…”

“…In Ref. , synchronization of dynamical networks with distributed delay is investigated via impulsive control. However, synchronization of networks with distributed delays has seldom been investigated using intermittent control.…”