Period-Doubling Bifurcation of Cycles in Retarded Functional Differential Equations

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Authors

ZÁTHURECKÝ Jakub

Year of publication 2023
Type Article in Periodical
Magazine / Source Journal of Dynamics and Differential Equations
MU Faculty or unit

Faculty of Science

Citation
Web https://doi.org/10.1007/s10884-023-10249-3
Doi http://dx.doi.org/10.1007/s10884-023-10249-3
Keywords Retarded functional differential equation; Delayed differential equation; Period-doubling bifurcation; Fredholm operator; Lyapunov-Schmidt reduction
Description A rigorous description of a period-doubling bifurcation of limit cycles in retarded functional differential equations based on tools of functional analysis and singularity theory is presented. Particularly, sufficient conditions for its occurrence and its normal form coefficients are expressed in terms of derivatives of the operator defining given equations. We also prove the exchange of stability in the case of a non-degenerate period-doubling bifurcation. The approach concerns Fredholm operators, Lyapunov-Schmidt reduction and recognition problem for pitchfork bifurcation.
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