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.
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This work was supported by the Russian Foundation for Basic Research, project no. 18-29-10043.
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Translated by I. Ruzanova
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Kashchenko, I.S. Influence of the Second Delay on Local Dynamics. Comput. Math. and Math. Phys. 60, 1261–1270 (2020). https://doi.org/10.1134/S0965542520080114
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DOI: https://doi.org/10.1134/S0965542520080114