高阶非线性高木-菅野模糊脉冲延迟耦合系统的稳定性

IF 3.2 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems Pub Date : 2024-10-22 DOI:10.1016/j.fss.2024.109164

Haoming Han , Shixu Zhao , Jing Zhang , Yan Liu

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引用次数: 0

摘要

在本研究中，我们考虑了高阶非线性高木-菅野模糊脉冲延迟耦合系统（TSFICSs）的稳定性。需要注意的是，在对高阶非线性 TSFICS 的研究中取消了线性增长条件，这与之前对脉冲系统的研究相比弱化了条件。此外，现有的研究方法对高阶非线性 TSFICS 不适用，因此建立了带有高阶项的新型脉冲微分不等式来研究高阶非线性 TSFICS 的稳定问题，并发展了高阶非线性情况下的经典脉冲微分不等式。接着，基于新的脉冲微分不等式，结合图论和 Lyapunov 方法，得到了稳定性的充分条件。最后，将理论结果应用于修正的脉冲延迟耦合 Fitzhugh-Nagumo 模型，并通过数值模拟来说明推导结果的实用价值。

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Stability of high-order nonlinear Takagi–Sugeno fuzzy impulsive delayed coupled systems

In this study, we consider the stability of high-order nonlinear Takagi–Sugeno fuzzy impulsive delayed coupled systems (TSFICSs). It should be noted that the linear growth condition is removed in the investigation of high-order nonlinear TSFICSs, which weakens the conditions compared with previous studies of impulsive systems. In addition, the existing research methods do not work for high-order nonlinear TSFICSs, so novel impulsive differential inequalities with high-order terms are established to investigate the stabilization of high-order nonlinear TSFICSs and develop the classic impulsive differential inequalities for high-order nonlinear situations. Next, sufficient conditions for the stability are obtained based on the new impulsive differential inequalities together with graph theory and the Lyapunov method. Finally, the theoretical results are applied to modified impulsive delayed coupled Fitzhugh–Nagumo models, and numerical simulations are provided to illustrate the practical value of the derived results.

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来源期刊

Fuzzy Sets and Systems 数学-计算机：理论方法

CiteScore

6.50

自引率

17.90%

发文量

321

审稿时长

6.1 months

期刊介绍： Since its launching in 1978, the journal Fuzzy Sets and Systems has been devoted to the international advancement of the theory and application of fuzzy sets and systems. The theory of fuzzy sets now encompasses a well organized corpus of basic notions including (and not restricted to) aggregation operations, a generalized theory of relations, specific measures of information content, a calculus of fuzzy numbers. Fuzzy sets are also the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling: fuzzy rule-based systems. Numerous works now combine fuzzy concepts with other scientific disciplines as well as modern technologies. In mathematics fuzzy sets have triggered new research topics in connection with category theory, topology, algebra, analysis. Fuzzy sets are also part of a recent trend in the study of generalized measures and integrals, and are combined with statistical methods. Furthermore, fuzzy sets have strong logical underpinnings in the tradition of many-valued logics.