Abstract

The local dynamics of singularly perturbed equations with two delays are studied in the case when both delays are asymptotically large and identical in the order of magnitude (proportional). Critical cases are identified, and all of them are shown to have an infinite dimension. To examine the behavior of solutions near the critical cases, special nonlinear equations—quasi-normal forms—are derived, whose solutions are asymptotic approximations to solutions of the original problem. The results are compared with those for single-delay equations.

中文翻译：

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第二延迟对局部动力学的影响

摘要

当两个时滞都渐近变大并且在数量级（比例）上相同时，研究了具有两个时滞的奇摄动方程的局部动力学。确定了关键案例，并且所有案例都显示为无穷大。为了检查临界情况附近的解的行为，导出了特殊的非线性方程（准正规形式），其解是对原始问题的解的渐近近似。将结果与单延迟方程的结果进行比较。