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 -