Exponential Synchronization of Linearly Coupled Neural Networks With Impulsive Disturbances

Abstract

of uncertain Hopfield neural networks with discrete and distributed delays," Phys. Lett. A, vol. 354, no. 4, pp. 288-297, Jun. 2006. [43] Z. Wang, Y. Liu, L. Yu, and X. Liu, "Exponential stability of delayed recurrent neural networks with Markovian jumping parameters," Phys. Lett. A, vol. 356, nos. 4-5, pp. 346-352, Aug. 2006. condition is closely related with the time delay, impulse strengths, average impulsive interval, and coupling structure of the systems. The obtained criterion is given in terms of an algebraic inequality which is easy to be verified, and hence our result is valid for largescale systems. The results extend and improve upon earlier work. As a numerical example, a small-world network composing of impulsive coupled chaotic delayed NN nodes is given to illustrate our theoretical result. Exponential Synchronization of Linearly Coupled Neural Networks with Impulsive Disturbances

Stability of delayed memristive neural networks with time-varying impulses

“…Therefore, memristive neural networks model with delays and impulsive effects should be more accurate to describe the evolutionary process of the system. 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.…”

“…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.…”

Synchronization of Coupled Neutral-Type Neural Networks With Jumping-Mode-Dependent Discrete and Unbounded Distributed Delays

“…While traditional neural networks have been successfully applied in static data-based classification and prediction problems for various engineering systems, the dynamical behaviors of the RNNs have recently gained a lot of research interests due to their capabilities of using dynamical temporal behavior to process arbitrary sequences of inputs. Motivated from both the basic science and the technological practice, the study of synchronization problems among an array of neural networks has been an active topic of research in the past few years, see [13], [15], [20], [22], [23] for some recent publications. Note that the original notion of synchronization dates back to the 1980s after the theory of deterministic chaos has been developed.…”

$H_{\infty}$ State Estimation for Discrete-Time Complex Networks With Randomly Occurring Sensor Saturations and Randomly Varying Sensor Delays

“…As a result, a number of dynamics analysis issues have been extensively investigated for complex networks such as the stability and stabilization, synchronization, pinning control and spread mechanism, see e.g. [1], [2], [4], [8], [10], [12], [14], [17], [18], [20], [21], [23]- [26], [29], [31], [34], [35] and the references therein.…”