Journal article
Bifurcation structure of the C-type period-doubling transition
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.
Language: | English |
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Year: | 2012 |
Pages: | 488-496 |
ISSN: | 18728022 and 01672789 |
Types: | Journal article |
DOI: | 10.1016/j.physd.2011.11.004 |