On global stability of nonlinear systems with unbounded and distributed delays and a dominating non-delay term

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-01-09 DOI:10.1016/j.cnsns.2025.108590

Elena Braverman , Cemil Tunç , Osman Tunç

引用次数: 0

Abstract

A system with, generally, unbounded and non-continuous delays is considered as a perturbation of a linear non-delay system. Boundedness of solutions, stability, global asymptotic stability, uniform exponential stability are established with a variety of methods, including designing a Lyapunov–Krasovskii functional and integral transformations. The system incorporates a linear non-delay part and a sum of either linear or nonlinear terms, dependent on several time-variable delays. The dependency of the stability type on the delay properties is outlined and illustrated with examples.

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具有无界分布时滞和非时滞项的非线性系统的全局稳定性

一般来说，无界和非连续延迟的系统被视为线性非延迟系统的扰动。通过设计 Lyapunov-Krasovskii 函数和积分变换等多种方法，确定了解的有界性、稳定性、全局渐近稳定性和均匀指数稳定性。该系统包含线性非延迟部分和线性或非线性项的总和，取决于几个时变延迟。本文概述了稳定性类型对延迟特性的依赖性，并通过实例进行了说明。

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.