Period-Doubling Bifurcation of Cycles in Retarded Functional Differential Equations

Varování

Publikace nespadá pod Fakultu sportovních studií, ale pod Přírodovědeckou fakultu. Oficiální stránka publikace je na webu muni.cz.

Autoři	ZÁTHURECKÝ Jakub
Rok publikování	2023
Druh	Článek v odborném periodiku
Časopis / Zdroj	Journal of Dynamics and Differential Equations
Fakulta / Pracoviště MU	Přírodovědecká fakulta
Citace
www	https://doi.org/10.1007/s10884-023-10249-3
Doi	http://dx.doi.org/10.1007/s10884-023-10249-3
Klíčová slova	Retarded functional differential equation; Delayed differential equation; Period-doubling bifurcation; Fredholm operator; Lyapunov-Schmidt reduction
Popis	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.
Související projekty:	Applications of Functional Analysis and Singularity Theory to Bifurcation Theory