Robust Stability of Complex-Valued Stochastic Neural Networks with Time-Varying Delays and Parameter Uncertainties

Abstract

In practical applications, stochastic effects are normally viewed as the major sources that lead to the system’s unwilling behaviours when modelling real neural systems. As such, the research on network models with stochastic effects is significant. In view of this, in this paper, we analyse the issue of robust stability for a class of uncertain complex-valued stochastic neural networks (UCVSNNs) with time-varying delays. Based on the real-imaginary separate-type activation function, the original UCVSNN model is analysed using an equivalent representation consisting of two real-valued neural networks. By constructing the proper Lyapunov–Krasovskii functional and applying Jensen’s inequality, a number of sufficient conditions can be derived by utilizing It o ^ ’s formula, the homeomorphism principle, the linear matrix inequality, and other analytic techniques. As a result, new sufficient conditions to ensure robust, globally asymptotic stability in the mean square for the considered UCVSNN models are derived. Numerical simulations are presented to illustrate the merit of the obtained results.

New feedback control techniques of quaternion fuzzy neural networks with time‐varying delay

“…Remark Serval dynamics of neural networks models without fuzzy terms have been examined in previous studies 1,72,73 . In this study, we not only focus on the finite‐time and fixed‐time stabilization of fuzzy neural networks by using the same method proposed in References 1,72,73 but also extend our results to the quaternion domain. As such, the approach proposed in this article is more general and powerful.…”

Stability of a Three-Species Cooperative System with Time Delays and Stochastic Perturbations

“…Proof. Applying the same manner as before, consider the linear system (26) and define V 1 , V 2 , and V 3 as before. By using the Itô formula and computing the derivatives of V 1 , V 2 , and V 3 along solutions of (26), then x 2 3 (s)ds,…”

“…In this paper, we assume time delays are constants, whereas in practice, time delays may be time-varying (see [25][26][27]), so it is necessary to study the dynamics with timevarying delays. Furthermore, for multispecies predator-prey system or multispecies competitive system, whether some similar results can be obtained?…”

Window of multistability and its control in a simple 3D Hopfield neural network: application to biomedical image encryption

“…In the engineering science domain, the applications of CVNN models have been reported by many researchers, e.g., for sonic wave, electromagnetic wave, light wave, quantum devices, image processing as well as signal processing. In regard to both the mathematical analysis and practical application, CVNN models have been widely studied, and many effective methods on various dynamical analyses of CVNN models are available [ 4 , 5 ]. Mainly, the Hopfield type of neural network (HTNN) models has been considered a key development owing to their adaptive mathematical model capability, along with many powerful methods concerning the stability of HTNN models [ 4 – 7 ].…”