ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Kashchenko S. A., Tolbey A. O. Quasinormal forms for systems of two equations with large delay. Izvestiya VUZ. Applied Nonlinear Dynamics, 2024, vol. 32, iss. 6, pp. 782-795. DOI: 10.18500/0869-6632-003135, EDN: NITFSM

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Language: 
Russian
Heading: 
Bifurcation in Dynamical Systems. Deterministic Chaos. Quantum Chaos.
Article type: 
Article
UDC: 
517.9
DOI: 
10.18500/0869-6632-003135
EDN: 
NITFSM

Quasinormal forms for systems of two equations with large delay

Autors: 
Kashchenko Sergej Aleksandrovich, P. G. Demidov Yaroslavl State University
Tolbey A. O., P. G. Demidov Yaroslavl State University
Abstract: 

A system of two equations with delay is considered. The purpose of this work is to study the local dynamics of this system under the assumption that the delay parameter is sufficiently large. Critical cases in the problem of stability of an equilibrium state are identified and it is shown that they have infinite dimension.

Methods. The research is based on the use of special methods of infinite-dimensional normalization. Classical methods based on the application of the theory of invariant integral manifolds and normal forms turn out to be directly inapplicable.

Results. As the main results, special nonlinear boundary value problems are constructed, which play the role of normal forms. Their nonlocal dynamics determine the behavior of all solutions of the original system in the vicinity of the equilibrium state.
 

Key words: 
dynamics
stability
delay
quasinormal forms
singular perturbations
Acknowledgments: 
The study was supported by a grant from the Russian Science Foundation № 21-71-30011, https://rscf.ru/project/21-71-30011/.
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Received: 
15.06.2024
Accepted: 
01.08.2024
Available online: 
31.10.2024
Published: 
29.11.2024
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