Formal Setting for Period Doubling Bifurcation of Limit Cycles

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Formal Setting for Period Doubling Bifurcation of Limit Cycles
Original language description
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.
Czech name
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Czech description
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Project
<a href="/en/project/EF19_073%2F0016943" target="_blank" >EF19_073/0016943: Internal grant agency of Masaryk University</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
15th Chaotic Modeling and Simulation International Conference
ISBN
9783031270819
ISSN
2213-8684
e-ISSN
2213-8692
Number of pages
15
Pages from-to
381-395
Publisher name
Springer
Place of publication
Cham (Switzerland)
Event location
Athens (Greece)
Event date
Jun 14, 2022
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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