Formal Setting for Period Doubling Bifurcation of Limit Cycles

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F23%3A00131250" target="_blank" >RIV/00216224:14310/23:00131250 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/978-3-031-27082-6_27" target="_blank" >https://doi.org/10.1007/978-3-031-27082-6_27</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-031-27082-6_27" target="_blank" >10.1007/978-3-031-27082-6_27</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Formal Setting for Period Doubling Bifurcation of Limit Cycles

Popis výsledku v původním jazyce

A rigorous description of period doubling bifurcation of limit cycles in autonomous systems of first order differential equations based on tools of functional analysis and singularity theory is presented. It is an alternative approach which is independent of the theory of discrete-time dynamical systems, especially Poincaré sections. Particularly, sufficient conditions for its occurrence and its normal form coefficients are expressed in terms of derivatives of the operator defining given equations. Also, stability of solutions is analysed and it is related to particular derivatives of the operator. Our approach is an adjustment of techniques used by Golubitsky and Schaeffer (Singularities and Groups in Bifurcation Theory: Volume 1. Springer, New York, 1985) in the study of Hopf bifurcation and it can be considered as a theoretical background for calculations presented in Kuznetsov et al. (SIAM J. Numer. Anal. 43:1407–1435, 2006). The normal form of a vector field derived in Iooss (J. Differ. Equ. 76:47–76, 1988) is not needed, since a given differential equation is considered as an algebraic equation. The theory used here concerns Fredholm operators, Lyapunov-Schmidt reduction and recognition problem for pitchfork bifurcation.

Název v anglickém jazyce

Formal Setting for Period Doubling Bifurcation of Limit Cycles

Popis výsledku anglicky

A rigorous description of period doubling bifurcation of limit cycles in autonomous systems of first order differential equations based on tools of functional analysis and singularity theory is presented. It is an alternative approach which is independent of the theory of discrete-time dynamical systems, especially Poincaré sections. Particularly, sufficient conditions for its occurrence and its normal form coefficients are expressed in terms of derivatives of the operator defining given equations. Also, stability of solutions is analysed and it is related to particular derivatives of the operator. Our approach is an adjustment of techniques used by Golubitsky and Schaeffer (Singularities and Groups in Bifurcation Theory: Volume 1. Springer, New York, 1985) in the study of Hopf bifurcation and it can be considered as a theoretical background for calculations presented in Kuznetsov et al. (SIAM J. Numer. Anal. 43:1407–1435, 2006). The normal form of a vector field derived in Iooss (J. Differ. Equ. 76:47–76, 1988) is not needed, since a given differential equation is considered as an algebraic equation. The theory used here concerns Fredholm operators, Lyapunov-Schmidt reduction and recognition problem for pitchfork bifurcation.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

10100 - Mathematics

Projekt

<a href="/cs/project/EF19_073%2F0016943" target="_blank" >EF19_073/0016943: Interní grantová agentura Masarykovy univerzity</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

15th Chaotic Modeling and Simulation International Conference

ISBN

9783031270819

ISSN

2213-8684

e-ISSN

2213-8692

Počet stran výsledku

15

Strana od-do

381-395

Název nakladatele

Springer

Místo vydání

Cham (Switzerland)

Místo konání akce

Athens (Greece)

Datum konání akce

14. 6. 2022

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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