Finite time stability of nonlinear impulsive stochastic system and its application to neural networks

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-08-31 DOI:10.1016/j.cnsns.2024.108298

Jingying Liu, Quanxin Zhu

引用次数: 0

Abstract

In this paper, we employ the Lyapunov theory to generalize the finite time stability (FTS) results from general deterministic impulsive systems to impulsive stochastic time-varying systems, which overcomes inherent challenges. Sufficient conditions for the FTS of the system under stabilizing and destabilizing impulses are established by using the method of average dwell interval (ADT). For FTS of stabilizing impulses, we relax the constraint on the differential operator by allowing it to be indefinite rather than strictly negative or semi-negative definite. Furthermore, the theoretical results are applied to impulsive stochastic neural networks. Finally, two numerical examples are given to validate the reliability and practicability of the obtained results.

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非线性脉冲随机系统的有限时间稳定性及其在神经网络中的应用

本文采用李雅普诺夫理论，将一般确定性脉冲系统的有限时间稳定性（FTS）结果推广到脉冲随机时变系统，克服了固有的难题。利用平均驻留间隔（ADT）方法，建立了稳定和失稳脉冲下系统有限时间稳定性的充分条件。对于稳定脉冲的 FTS，我们放宽了对微分算子的限制，允许它是不确定的，而不是严格的负定或半负定。此外，我们还将理论结果应用于脉冲随机神经网络。最后，我们给出了两个数值示例，以验证所获结果的可靠性和实用性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.