Bifurcation structure of the C-type period-doubling transition
Publication: Research - peer-review › Journal article – Annual report year: 2012
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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
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TY - JOUR
T1 - Bifurcation structure of the C-type period-doubling transition
A1 - Laugesen,Jakob Lund
A1 - Mosekilde,Erik
A1 - Zhusubaliyev,Zhanybai T.
AU - Laugesen,Jakob Lund
AU - Mosekilde,Erik
AU - Zhusubaliyev,Zhanybai T.
PB - Elsevier BV North-Holland
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
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
SN - 0167-2789
IS - 5
VL - 241
SP - 488
EP - 496
ER -