含有大延迟的扩散耦合链

IF 0.6 4区数学 Q3 MATHEMATICS

Mathematical Notes Pub Date : 2024-07-05 DOI:10.1134/s0001434624030040

S. A. Kashchenko

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引用次数: 0

摘要

摘要我们研究了具有大量元素和包含大延迟的扩散耦合的振荡器系统的局部动力学。我们分离了零平衡态稳定性问题中的临界情况，并证明所有临界情况都是无限维的。利用特殊的无限归一化方法，我们构建了准正常形式，即抛物线类型的非线性边界值问题，其非局部动力学决定了原系统在平衡态小邻域内的解的行为。这些准正常形式包含两个或三个空间变量，强调了原问题动态特性的复杂性。

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Chains with Diffusion-Type Couplings Contaning a Large Delay

Abstract

We investigate the local dynamics of a system of oscillators with a large number of elements and with diffusion-type couplings containing a large delay. We isolate critical cases in the stability problem for the zero equilibrium state and show that all of them are infinite-dimensional. Using special infinite normalization methods, we construct quasinormal forms, that is, nonlinear boundary value problems of parabolic type whose nonlocal dynamics determines the behavior of solutions of the original system in a small neighborhood of the equilibrium state. These quasinormal forms contain either two or three spatial variables, which emphasizes the complexity of dynamic properties of the original problem.

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来源期刊

Mathematical Notes 数学-数学

CiteScore

0.90

自引率

16.70%

发文量

179

审稿时长

24 months

期刊介绍： Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.