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@inproceedings{2297925,
author = {Záthurecký, Jakub},
address = {Cham (Switzerland)},
booktitle = {15th Chaotic Modeling and Simulation International Conference},
doi = {http://dx.doi.org/10.1007/978-3-031-27082-6_27},
editor = {Skiadas, C.H., Dimotikalis, Y.},
keywords = {Limit cycle; Period doubling; Fredholm operator; Lyapunov-Schmidt reduction; Pitchfork bifurcation},
howpublished = {tištěná verze "print"},
language = {eng},
location = {Cham (Switzerland)},
isbn = {978-3-031-27081-9},
pages = {381-395},
publisher = {Springer},
title = {Formal Setting for Period Doubling Bifurcation of Limit Cycles},
url = {https://doi.org/10.1007/978-3-031-27082-6_27},
year = {2023}
}
TY - JOUR
ID - 2297925
AU - Záthurecký, Jakub
PY - 2023
TI - Formal Setting for Period Doubling Bifurcation of Limit Cycles
PB - Springer
CY - Cham (Switzerland)
SN - 9783031270819
KW - Limit cycle
KW - Period doubling
KW - Fredholm operator
KW - Lyapunov-Schmidt reduction
KW - Pitchfork bifurcation
UR - https://doi.org/10.1007/978-3-031-27082-6_27
N2 - 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.
ER -
ZÁTHURECKÝ, Jakub. Formal Setting for Period Doubling Bifurcation of Limit Cycles. In Skiadas, C.H., Dimotikalis, Y. \textit{15th Chaotic Modeling and Simulation International Conference}. Cham (Switzerland): Springer, 2023, s.~381-395. ISBN~978-3-031-27081-9. Dostupné z: https://dx.doi.org/10.1007/978-3-031-27082-6\_{}27.
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