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Izv. Vyssh. Uchebn. Zaved. Mat., 2018, Number 9, Pages 29–41 (Mi ivm9395)  

Analysis of local dynamics of difference and close to them differential-difference equations

I. S. Kashchenkoa, S. A. Kashchenkoab

a Yaroslavl State University named after P.G. Demidov, 14 Sovetskaya str., Yaroslavl, 150000 Russia
b National Research Nuclear University “MIFI”, 31 Kashirskoe Highway, Moscow, 115409 Russia

Abstract: We consider the local dynamics of a class nonlinear difference equations which is important for applications. Using the perturbation theory methods we built the sets of singularly perturbed differential-difference equations close to the original difference equations to some extent. We show that the critical cases in the problem of stability of a null balance state have infinite dimension. We offer the method to set special non-linear boundary-value problems that do not contain small parameters. They play the role of normal forms. Their nonlocal dynamics describes the structure of solutions to original equations in a small neighborhood of a balance state. We show that the dynamic properties of difference and close to them differential-difference equations considerably differ.

Keywords: bifurcation, stability, normal form, singular perturbation, dynamics.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 1.5722.2017/8.9


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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2018, 62:9, 24–34

Bibliographic databases:

UDC: 517.9
Received: 17.05.2017

Citation: I. S. Kashchenko, S. A. Kashchenko, “Analysis of local dynamics of difference and close to them differential-difference equations”, Izv. Vyssh. Uchebn. Zaved. Mat., 2018, no. 9, 29–41; Russian Math. (Iz. VUZ), 62:9 (2018), 24–34

Citation in format AMSBIB
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\by I.~S.~Kashchenko, S.~A.~Kashchenko
\paper Analysis of local dynamics of difference and close to them differential-difference equations
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2018
\issue 9
\pages 29--41
\mathnet{http://mi.mathnet.ru/ivm9395}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2018
\vol 62
\issue 9
\pages 24--34
\crossref{https://doi.org/10.3103/S1066369X18090049}
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  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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