Exponential synchronization of memristive Cohen–Grossberg neural networks with mixed delays

Abstract

This paper concerns the problem of global exponential synchronization for a class of memristor-based Cohen-Grossberg neural networks with time-varying discrete delays and unbounded distributed delays. The driveresponse set is discussed. A novel controller is designed such that the response (slave) system can be controlled to synchronize with the drive (master) system. Through a nonlinear transformation, we get an alternative system from the considered memristor-based Cohen-Grossberg neural networks. By investigating the global exponential synchronization of the alternative system, we obtain the corresponding synchronization criteria of the considered memristor-based Cohen-Grossberg neural networks. Moreover, the conditions established in this paper are easy to be verified and improve the conditions derived in most of existing papers concerning stability and synchronization for memristorbased neural networks. Numerical simulations are given to show the effectiveness of the theoretical results.

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.…”

“…As a result, Cohen-Grossberg neural networks have attracted considerable research attention and many good results related have been reported on the boundedness, stability, convergence, synchronization and other oscillatory properties of Cohen-Grossberg neural networks (Cao and Liang 2004;Lisena 2011;Zhu and Cao 2010;. In addition, it has been reported that the memristorbased neural networks can exhibit some complicated dynamics and even chaotic behavior, and synchronization of chaotic neural networks based on memristor has also become an important area of study (Yang et al 2014;Wu et al 2012;Wen et al 2013;Li and Cao 2015;Shen 2013, 2014;Bao and Cao 2015).…”

“…In Yang et al (2014), by nonlinear transformation, the authors studied the exponential synchronization of memristor-based Cohen-Grossberg neural network by using novel discontinuous feedback controller. 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.…”

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;.…”