Global exponential stability and periodicity of reaction–diffusion recurrent neural networks with distributed delays and Dirichlet boundary conditions

Global exponential synchronization of delayed BAM neural networks with reaction-diffusion terms and the Neumann boundary conditions

“…It is noted that we construct a novel Lyapunov functional here as defined in (20) since the considered model contains time-varying and distributed delays and reaction-diffusion terms. We can see that the results and research method obtained in this article can also be extended to many other types of NNs with reaction-diffusion terms, e.g., the cellular NNs, cohen-grossberg NNs, etc.…”

“…Therefore, we must consider that the activations vary in space as well as in time. In [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27], the authors have considered various dynamical behaviors such as the stability, periodic oscillation, and synchronization of NNs with diffusion terms, which are expressed by partial differential equations. For instance, the authors of [16] discuss the impulsive control and synchronization for a class of delayed reaction-diffusion NNs with the Dirichlet boundary conditions in terms of p-norm.…”

Delay-dependent exponential stability for impulsive Cohen–Grossberg neural networks with time-varying delays and reaction–diffusion terms

“…[13][14][15][17][18][19][20][21][22][23][24][25], we do not know the reaction-diffusion phenomenon how to affect stability of neural networks. Recently, Lu et al proposed some reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions and obtained some diffusion-dependent criteria on stability and periodicity for the formulated neural networks [26][27][28], these criteria show that the diffusion phenomenon is beneficial to the stabilization of neural systems. To the best of our knowledge, few authors have investigated impulsive Cohen-Grossberg cellular neural networks with time-varying delays, reaction-diffusion terms and the Dirichlet boundary conditions.…”

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

“…The neural networks with diffusion terms can commonly be expressed by partial differential equations [10][11][12][13][14][15] have considered the stability of neural networks with diffusion terms, in which boundary conditions are all the Neumann boundary conditions. The neural networks model with Dirichlet boundary conditions has been considered in [16,21], but it concentrated on deterministic systems and did not take random perturbation into consideration. To the best of our knowledge, few authors have considered global exponential stability in the mean square of stochastic reaction-diffusion recurrent neural networks with continuously distributed delays and Dirichlet boundary conditions.…”

“…Motivated by these, the stability of stochastic reaction-diffusion neural networks with both continuously distributed delays and Dirichlet boundary conditions is studied in this paper. We use a similar method as in [21], but deal with a more general case in which stochastic perturbations are concerned. The influence of diffusion, continuously distributed delays upon the stability of the concerned system is also discussed.…”