具有额外内部耦合的扩散耦合微分方程系统的动态特性

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Theoretical and Mathematical Physics Pub Date : 2024-08-26 DOI:10.1134/S0040577924080038

L. I. Ivanovskiy

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引用次数: 0

摘要

摘要我们研究了具有扩散相互作用和附加内部耦合的微分方程系统的动力学。这类系统非常有趣，因为附加耦合处系数的微小变化就能获得错综复杂的相重排情景。对于所研究的系统，我们找到了参数的临界依赖性，这样零平衡就失去了稳定性，因为在一种情况下会出现两个空间不均匀状态，而在另一种情况下会出现一个循环。当参数值接近临界值时，我们就可以得到零解分支状态的渐近公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Dynamical properties of a diffusion-coupled system of differential equations with an additional internal coupling

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Dynamical properties of a diffusion-coupled system of differential equations with an additional internal coupling

We study the dynamics of a system of differential equations with the diffusion interaction and an additional internal coupling. Such systems are interesting because a slight variation in the coefficient at the additional coupling allows obtaining intricate scenarios of phase rearrangements. For the system under study, we find the critical dependence of the parameters such that zero equilibrium loses stability as two spatially inhomogeneous states appear in one case and a cycle in another case. With the parameter values close to the critical ones, asymptotic formulas are obtained for the regimes that branch off from the zero solution.

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来源期刊

Theoretical and Mathematical Physics 物理-物理：数学物理

CiteScore

1.60

自引率

20.00%

发文量

103

审稿时长

4-8 weeks

期刊介绍： Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems. Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.