Fixed-Time Synchronization of Reaction-Diffusion Fuzzy Neural Networks with Stochastic Perturbations

Abstract

In this paper, we investigated the fixed-time synchronization problem of a type of reaction-diffusion fuzzy neural networks with stochastic perturbations by developing simple control schemes. First, some generalized fixed-time stability results are introduced for stochastic nonlinear systems. Based on these results, some generic fixed-time stability criteria are established and upper bounds of settling time are directly calculated by using several special functions. Then, the fixed-time synchronization of a type of reaction-diffusion fuzzy neural networks with stochastic perturbations is analysed by designing a type of controller which is more simple and thus have a better applicability. Finally, one numerical example with its Matlab simulations is provided to show the feasibility of developed theoretical results.

Stochastic Synchronization of Impulsive Reaction–Diffusion BAM Neural Networks at a Fixed and Predetermined Time

“…This convergence is more precise than the time T 2 mentioned in Theorem 1. When compared to the previous works referenced in [38,39,41,43], the findings in this paper offer a more practical and applicable approach.…”

“…However, fuzziness is often unavoidable in numerous dynamical systems. It can allow the network to handle uncertain and ambiguous information, thereby improving its robustness and adaptability [31,38,41]. In this paper, we did not consider fuzzy terms.…”

“…In previous studies [37,38], the authors demonstrated the synchronization of FXT in BAM neural networks incorporating a reaction-diffusion term. In the course of their work, they employed the inequality X udx p ≤ X u p dx for u ∈ X, p ≥ 1, with X as a bounded compact set with a smooth boundary ∂X.…”

“…In previous studies [32][33][34]38,41], researchers have successfully achieved FXT and PDT synchronization in different types of impulsive neural networks. However, there is a lack of research on PDT synchronization in stochastic impulsive reaction-diffusion BAM neural networks.…”

Fixed/Preassigned-Time Synchronization of Fully Quaternion-Valued Cohen–Grossberg Neural Networks with Generalized Time Delay

“…In order to address this challenge, the concept of fixed time (FIT) was introduced and the FIT stability theorem was first proposed in [17], in which the estimate of the ST is improved by eliminating its dependence on initial values. Since then, numerous remarkable research endeavors have emerged, encompassing FIT synchronization of recurrent neural networks [18][19][20], complex-valued neural networks (CVNNs) [21][22][23], and QVNNs [24][25][26][27][28]. In [24][25][26], the FIT synchronization of QVNNs was investigated by decomposing the QVNN model into four real valued neural networks, which resulted in four real-valued controllers being designed.…”