Bifurcation structure of the C-type period-doubling transition

Publication: Research - peer-review › Journal article – Annual report year: 2012

Standard

Bifurcation structure of the C-type period-doubling transition. / Laugesen, Jakob Lund ; Mosekilde, Erik; Zhusubaliyev, Zhanybai T.

In: Physica D: Nonlinear Phenomena, Vol. 241, No. 5, 2012, p. 488-496.

Publication: Research - peer-review › Journal article – Annual report year: 2012

In: Physica D: Nonlinear Phenomena, Vol. 241, No. 5, 2012, p. 488-496.

Publication: Research - peer-review › Journal article – Annual report year: 2012

Bibtex

@article{41ca9ee553584b30bd5d9fe8dde4273f,

title = "Bifurcation structure of the C-type period-doubling transition",

keywords = "Transverse period-doubling cascades, Bifurcation structure, Torus doubling bifurcations, Multi-dimensional dynamics, Multi-layered tori, Forced period-doubling systems",

author = "Laugesen, {Jakob Lund} and Erik Mosekilde and Zhusubaliyev, {Zhanybai T.}",

year = "2012",

doi = "10.1016/j.physd.2011.11.004",

volume = "241",

pages = "488--496",

journal = "Physica D: Nonlinear Phenomena",

issn = "0167-2789",

publisher = "Elsevier BV North-Holland",

number = "5",

}

RIS

TY - JOUR

T1 - Bifurcation structure of the C-type period-doubling transition

AU - Laugesen,Jakob Lund

AU - Mosekilde,Erik

AU - Zhusubaliyev,Zhanybai T.

PY - 2012

Y1 - 2012

N2 - 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 Rössler 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.

AB - 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 Rössler 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.

KW - Transverse period-doubling cascades

KW - Bifurcation structure

KW - Torus doubling bifurcations

KW - Multi-dimensional dynamics

KW - Multi-layered tori

KW - Forced period-doubling systems

U2 - 10.1016/j.physd.2011.11.004

DO - 10.1016/j.physd.2011.11.004

M3 - Journal article

VL - 241

SP - 488

EP - 496

JO - Physica D: Nonlinear Phenomena

T2 - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 5

ER -