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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2020, Volume 60, Number 8, Pages 1304–1314
DOI: https://doi.org/10.31857/S0044466920080116 (Mi zvmmf11112) 		 
Influence of the second delay on local dynamics

I. S. Kashchenko

Yaroslavl State University, Yaroslavl, 150003 Russia
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DOI: https://doi.org/10.31857/S0044466920080116
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.
Funding agency Grant number
Russian Foundation for Basic Research 18-29-10043
Received: 15.11.2019
Revised: 14.01.2020
Accepted: 09.04.2020
English version:
Computational Mathematics and Mathematical Physics, 2020, Volume 60, Issue 8, Pages 1261–1270
DOI: https://doi.org/10.1134/S0965542520080114
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: I. S. Kashchenko, “Influence of the second delay on local dynamics”, Zh. Vychisl. Mat. Mat. Fiz., 60:8 (2020), 1304–1314; Comput. Math. Math. Phys., 60:8 (2020), 1261–1270
Citation in format AMSBIB
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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