Bifurcation structure of the -type period-doubling transition

Autor:	Jakob Lund Laugesen, Erik Mosekilde, Zhanybai T. Zhusubaliyev
Rok vydání:	2012
Předmět:	Period-doubling bifurcation Transcritical bifurcation Pitchfork bifurcation Classical mechanics Arnold tongue Statistical and Nonlinear Physics Saddle-node bifurcation Bogdanov–Takens bifurcation Condensed Matter Physics Bifurcation diagram Bifurcation Mathematics
Zdroj:	Physica D: Nonlinear Phenomena. 241:488-496
ISSN:	0167-2789
DOI:	10.1016/j.physd.2011.11.004
Popis:	The period-doubling transition to chaos along the edge of an Arnold tongue is known to display unusual organization and scaling behavior (Kuznetsov et al. (2005) [7] ). It is also known that forced period-doubling systems may be associated with the appearance of so-called period-doubled tori (Arneodo et al. (1983) [15] ). Using the Rossler system as an example, we present a detailed analysis of the bifurcation structure associated with the forcing of a three-dimensional period-doubling system. We explain how this structure is related to the recently discovered phenomenon of multi-layered tori and discuss different bifurcation scenarios that transform a resonance torus into a period-doubled ergodic torus. Similar bifurcation phenomena have recently been observed in a biologically relevant model of kidney blood flow regulation in response to fluctuations in arterial pressure.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::c2b0cec2a75da90bcdde3fd8338784f1 https://doi.org/10.1016/j.physd.2011.11.004 Zobrazit plný text záznamu Full Text from ScienceDirect