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.
Key words:delay equation, two delays, small parameter, singular perturbation, asymptotics, normal form, dynamics.
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