Intermittent Impulsive Synchronization of Chaotic Delayed Neural Networks

Abstract

In this paper, a novel intermittent impulsive synchronization scheme is proposed to realize synchronization of two chaotic delayed neural networks. Intermittent impulsive control breaks through the limitation of the upper bound of the impulsive intervals in general impulsive control. In our synchronization scheme, impulsive control is only activated in the control windows, rather than during the whole time. Several synchronization criteria for chaotic delayed neural networks are established utilizing the method of linear matrix inequalities (LMI) and the Lyapunov-Razumikhin technique. Two numerical examples are given to demonstrate the effectiveness of our main results.

Stability of delayed memristive neural networks with time-varying impulses

“…During the last few years, there has been increasing interest in the stability problem in delayed impulsive neural networks (Lu et al 2010;Hu et al 2012;Chen and Zheng 2009;Yang and Xu 2007;Liu and Liu 2007;Liu et al 2011;Lu et al 2011Lu et al , 2012Guan et al 2006;Yang and Xu 2005;Zhang et al 2006). In Liu et al (2011), synchronization for nonlinear stochastic dynamical networks was investigated using pinning impulsive strategy. In Guan et al (2006), a new class of hybrid impulsive models has been introduced and some good results about asymptotic stability properties have been obtained by using the ''average dwell time'' concept.…”

“…Conversely, an impulsive is said to be stabilizing if it can enhance the stability of dynamic systems. Stability of neural networks with stabilizing impulses or destabilizing has been studied in many papers (Lu et al 2010;Hu et al 2012;Chen and Zheng 2009;Yang and Xu 2007;Liu and Liu 2007;Liu et al 2011;Lu et al Lu et al 2011Guan et al 2006;Yang and Xu 2005;Zhang et al 2006). When the impulsive effects are stabilizing, the frequency of the impulses should not be too low.…”

“…When the impulsive effects are stabilizing, the frequency of the impulses should not be too low. In most of the literature (Lu et al 2010;Hu et al 2012;Chen and Zheng 2009;Yang and Xu 2007;Liu and Liu 2007;Liu et al 2011;Lu et al 2011Lu et al , 2012Guan et al 2006;Yang and Xu 2005) only investigate the stability problem when the impulses are stabilizing and the upper bound of the impulse intervals is used to guarantee the frequency of the impulses. When the impulsive effects are destabilizing, the lower bound of the impulsive intervals can be used to ensure that the impulses do not occur too frequently.…”

Robust impulsive synchronization of Lorenz chaotic dynamical system with capability of unknown bounded disturbance rejection

“…Criteria for synchronization and stability are provided with Halanay delayed differential equation [8]. In [9] Periodic impulsive synchronization of two delayed chaotic neural networks is noticed. Several synchronization conditions of delayed chaotic neural networks are alleged via LMI approach and Lyapunov-Razumikhin techniques.…”

Leader-following consensus of a class of stochastic delayed multi-agent systems with partial mixed impulses

“…Based on the proposed three types of partial mixed impulses, the global mean square leader-following consensus problem is investigated for a class of stochastic networked multi-agent systems with unknown time-varying delays. Compared with the works of impulsive effects in uncoupled dynamical systems (Liu, Shen, & Zhang, 2011;Yang & Xu, 2007), complex networks (Guan, Liu, Feng, & Wang, 2010;Liu & Hill, 2011;Liu et al, 2013;Lu et al, 2012;Zhang, Tang et al, 2013) and networked control systems (Goebel et al, 2009;Nešić & Teel, 2004;Zhang, Gao et al, 2013), the main contributions of this paper are mainly threefold: (1) a novel concept of partial mixed impulses is proposed for the first time, which can encompass several well-known impulses (Guan et al, 2010;Liu & Hill, 2011;Lu et al, 2012;Yang & Xu, 2007);…”