Delay-independent stability of stochastic reaction–diffusion neural networks with Dirichlet boundary conditions

Abstract

This paper deals with the problem of global stability of stochastic reaction-diffusion recurrent neural networks with continuously distributed delays and Dirichlet boundary conditions. The influence of diffusion, noise and continuously distributed delays upon the stability of the concerned system is discussed. New stability conditions are presented by using of Lyapunov method, inequality techniques and stochastic analysis. Under these sufficient conditions, globally exponential stability in the mean square holds, regardless of system delays. The proposed results extend those in the earlier literature and are easier to verify.

Stability analysis for delayed genetic regulatory networks with reaction--diffusion terms

“…1, the issue on stability analysis of reaction-diffusion GRNs has not yet been addressed in the literature. But many results on the problem of stability for reaction-diffusion neural networks are available in the literature [15,16,18,31,32,34] . However, all criteria of them are delay independent.…”

“…Therefore, it is necessary to take time delays and uncertainties into account in stability analysis of GRNs. The problems on stability analysis and synchronization of delayed neural networks and complex networks have been extensively investigated during the past decades [10,11,15,16,20,37]. Recently, many significant results on the stability issue of delayed GRNs have been published in the literature; see, for example, [1,13,17,22,23,27,30,33,38] and the references therein.…”

Exponential synchronization for reaction-diffusion neural networks with mixed time-varying delays via periodically intermittent control

“…From the above analysis, the stochastic noise perturbation and diffusion effects on dynamic behaviors of neural networks cannot be neglected, so the theoretical results on dynamic behaviors including stochastic disturbance and diffusion parameters are more reasonable. With respect to reaction-diffusion neural networks with stochastic perturbation, a few results about the dynamic analysis have been reported in the literature [26][27][28][29][30][31][32][33][34][35].…”

Synchronization of stochastic chaotic neural networks with reaction-diffusion terms

“…Therefore, it is reasonable and significant to take reaction-diffusion effect into full account in the research of neural networks. Many results on stability analysis of reactiondiffusion neural networks have been presented in the literature; see, for example, [5,19,23,25,27,35,36,38,39] and the references therein.…”