In this paper, we study stochastic impulsive reaction-diffusion neural networks with S-type distributed delays, aiming to obtain the sufficient conditions for global exponential stability. First, an impulsive inequality involving infinite delay is introduced and the asymptotic behaviour of its solution is investigated by the truncation method. Then, global exponential stability in the mean-square sense of the stochastic impulsive reaction-diffusion system is studied by constructing a simple Lyapunov-Krasovskii functional where the S-type distributed delay is handled by the impulsive inequality. Numerical examples are also given to verify the effectiveness of the proposed results. Finally, the obtained theoretical results are successfully applied to an image encryption scheme based on bit-level permutation and the stochastic neural networks.

It is of vital importance to understand the population structure, dissect the genetic bases of performance traits, and make proper strategies for selection in breeding programs. However, there is no single webserver covering the specific needs in aquaculture. We present Aquaculture Molecular Breeding Platform (AMBP), the first web server for genetic data analysis in aquatic species of farming interest. AMBP integrates the haplotype reference panels of 18 aquaculture species, which greatly improves the accuracy of genotype imputation. It also supports multiple tools to infer genetic structures, dissect the genetic architecture of performance traits, estimate breeding values, and predict optimum contribution. All the tools are coherently linked in a web-interface for users to generate interpretable results and evaluate statistical appropriateness. The webserver supports standard VCF and PLINK (PED, MAP) files, and implements automated pipelines for format transformation and visualization to simplify the process of analysis. As a demonstration, we applied the webserver to Pacific white shrimp and Atlantic salmon datasets. In summary, AMBP constitutes comprehensive resources and analytical tools for exploring genetic data and guiding practical breeding programs. AMBP is available at http://mgb.qnlm.ac.

This article studies the practical exponential stability of impulsive stochastic reaction-diffusion systems (ISRDSs) with delays. First, a direct approach and the Lyapunov method are developed to investigate the pth moment practical exponential stability and estimate the convergence rate. Note that these two methods can also be used to discuss the exponential stability of systems in certain conditions. Then, the practical stability results are successfully applied to the impulsive reaction-diffusion stochastic Hopfield neural networks (IRDSHNNs) with delays. By the illustration of four numerical examples and their simulations, our results in this article are proven to be effective in dealing with the problem of practical exponential stability of ISRDSs with delays, and may be regarded as stabilization results.

This brief investigates nonautonomous stochastic reaction-diffusion neural-network models with S-type distributed delays. First, the existence and uniqueness of mild solution are studied under the Lipschitz condition without the linear growth condition. Due to the existence of a nonautonomous reaction-diffusion term and the infinite dimensional Wiener process, the criteria for the well-posedness of the models are established based on the evolution system theory. Then, the S-type distributed delay, which is an infinite delay, is handled by the truncation method, and sufficient conditions for the global exponential stability are obtained by constructing a simple Lyapunov-Krasovskii functional candidate. Finally, neural-network examples and an illustrative example are given to show the applications of the obtained results.