Stability of delayed memristive neural networks with time-varying impulses

Abstract

This paper addresses the stability problem on the memristive neural networks with time-varying impulses. Based on the memristor theory and neural network theory, the model of the memristor-based neural network is established. Different from the most publications on memristive networks with fixed-time impulse effects, we consider the case of time-varying impulses. Both the destabilizing and stabilizing impulses exist in the model simultaneously. Through controlling the time intervals of the stabilizing and destabilizing impulses, we ensure the effect of the impulses is stabilizing. Several sufficient conditions for the globally exponentially stability of memristive neural networks with time-varying impulses are proposed. The simulation results demonstrate the effectiveness of the theoretical results.

Event-based exponential synchronization of complex networks

“…Thus, it is necessary to implement discrete-time controllers. The impulsive controllers (Yang 2001;Lu et al 2013Lu et al , 2010Tan et al 2015;Qi et al 2014;Pu et al 2015) and the sampled data controllers (Chen and Francis 1995;Yu et al 2013bYu et al , 2011a are two typical types of controllers with discrete time updates. In Å ström and Bernhardsson (2002) andÅ ström (2008), the authors proposed the event-triggered controllers.…”

Function projective synchronization of memristor-based Cohen–Grossberg neural networks with time-varying delays

“…Since the successful fabrication of physical memristive device by the scientists at Hewlett-Packard Labs in 2008 (Strukov et al 2008), witch its existence was firstly predicted by Leon Chua in 1971(Chua 1971, various types of models of networks based on memristor have been designed and analyzed (Itoh and Chua 2010;Oskoee and Sahimi 2011;Corinto et al 2011;Buscarino et al 2012;Pershin and Ventra 2012;Pershin et al 2013;Yang et al 2014;Qi et al 2014). Especially, the memristor-based neural networks has been one of the most active research areas and has attracted the attention of many researchers (Itoh and Chua 2010;Pershin and Ventra 2012;Yang et al 2014;Qi et al 2014;Chandrasekar et al 2014;Wan and Cao 2015).…”

“…Especially, the memristor-based neural networks has been one of the most active research areas and has attracted the attention of many researchers (Itoh and Chua 2010;Pershin and Ventra 2012;Yang et al 2014;Qi et al 2014;Chandrasekar et al 2014;Wan and Cao 2015). Memristor-based neural network can remember its past dynamical history, store a continuous set of states, and be ''plastic'' according to the pre-synaptic and postsynaptic neuronal activity (Strukov et al 2008;Qi et al 2014), an ideal tool to mimic the functionalities of the human brain.…”

“…In Qi et al (2014), by employing the differential inclusion theory and the Lyapunov method, the authors investigated the stability problem for a class of general memristor-based neural networks with time-varying delay and time-varying impulses. In Rakkiyappan et al (2015), by using Banach contraction principle, differential inclusion and framework of Filippov solution, the authors concerned the stability problem of a class of memristor-based fractional-order neural networks with time delay and different types of memductance functions.…”

The stability of impulsive stochastic Cohen–Grossberg neural networks with mixed delays and reaction–diffusion terms

“…In recent years, CGNN, which includes the famous Hopfield neural networks, cellular neural networks and Lotka-Volterra competition models as its special cases, has received extensive attention because of great range of applications in many areas such as optimization, pattern recognition, associative memory, robotics and computer vision. In such application, it is of prime importance to ensure that the designed neural networks is stable (Zhang and Wang 2008;Yang and Cao 2014;Qi et al 2014;Zhou et al 2007;Li andSong 2008, 2013;Li and Shen 2010;.…”