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Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 8, Pages 1304–1314 (Mi zvmmf11112)  

Influence of the second delay on local dynamics

I. S. Kashchenko

Yaroslavl State University, Yaroslavl, 150003 Russia

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


DOI: https://doi.org/10.31857/S0044466920080116


English version:
Computational Mathematics and Mathematical Physics, 2020, 60:8, 1261–1270

Bibliographic databases:

UDC: 517.9
Received: 15.11.2019
Revised: 14.01.2020
Accepted:09.04.2020

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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\pages 1261--1270
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