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Corporate Dynamics in Chains of Coupled Logistic Equations with Delay
Computational Mathematics and Mathematical Physics ( IF 0.7 ) Pub Date : 2021-08-22 , DOI: 10.1134/s0965542521070083
S. A. Kashchenko 1
Affiliation  

Abstract

The local dynamics of coupled chains of identical oscillators are considered. As a basic model of an oscillator, the well-known logistic equation with delay is proposed. The transition to studying a spatially distributed model is made. Two types of coupling of major interest are treated: diffusive coupling and unidirectional coupling. Critical cases are distinguished in the stability problem for the equilibrium state. It turns out that they are of infinite dimension: infinitely many roots of the characteristic equation tend to the imaginary axis as a small parameter characterizing the inverse of the number of elements in the chain tends to zero. The main result is the constructed special nonlinear boundary value problems whose nonlocal dynamics describes the behavior of all solutions for the chain in a neighborhood of the equilibrium state.



中文翻译:

时滞耦合逻辑方程链中的企业动力学

摘要

考虑了相同振荡器的耦合链的局部动力学。作为振荡器的基本模型,提出了众所周知的带有延迟的逻辑方程。过渡到研究空间分布模型。主要关注两种类型的耦合:扩散耦合和单向耦合。临界情况在平衡状态的稳定性问题中是有区别的。事实证明,它们是无限维的:特征方程的无穷多个根趋向于虚轴,作为表征链中元素数量倒数的小参数趋于零。主要结果是构建了特殊的非线性边值问题,其非局部动力学描述了链在平衡状态附近的所有解的行为。

更新日期:2021-08-23
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