Abstract

We study a two-dimensional singularly perturbed system with delay, which is a simplification of models used in laser physics. We analyze several cases of a small parameter multiplying the derivative in the first equation and investigate the behavior of solutions in a neighborhood of a stationary point when the system parameters pass through bifurcation values. Methods for local asymptotic analysis are used to construct special nonlinear equations describing the structure of solutions and the asymptotic approximation of solutions of the original problem.

中文翻译：

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两个时滞微分方程奇摄动系统的动力学

摘要

我们研究了具有延迟的二维奇异摄动系统，这是激光物理学中使用的模型的简化。我们分析了小参数乘以第一个方程中的导数的几种情况，并研究了当系统参数通过分岔值时在驻点附近的解的行为。局部渐近分析方法用于构造描述解的结构和原问题解的渐近逼近的特殊非线性方程。