Abstract

The local dynamics of systems of two equations with delay is considered. The main assumption is that the delay parameter is large enough. Critical cases in the problem of the stability of the equilibrium state are identified, and it is shown that they are of infinite dimension. Methods of infinite-dimensional normalization are used and further developed. The main result is the construction of special nonlinear boundary value problems that play the role of normal forms. Their nonlocal dynamics determine the behavior of all solutions of the original system in a neighborhood of the equilibrium state.

中文翻译：

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大时滞两个方程组的动力学

摘要

考虑具有时滞的两个方程组的局部动力学。主要假设是延迟参数足够大。确定了平衡状态稳定性问题中的关键情况，并表明它们具有无限维数。使用并进一步发展了无限维归一化方法。主要结果是构建发挥正常形式作用的特殊非线性边值问题。它们的非局部动力学决定了原始系统在平衡状态邻域中的所有解的行为。