Bifurcation structure of the C-type period-doubling transition

Jakob Lund Laugesen, Erik Mosekilde, Zhanybai T. Zhusubaliyev

Research output: Contribution to journalJournal articleResearchpeer-review


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.
Original languageEnglish
JournalPhysica D: Nonlinear Phenomena
Issue number5
Pages (from-to)488-496
Publication statusPublished - 2012


  • Transverse period-doubling cascades
  • Bifurcation structure
  • Torus doubling bifurcations
  • Multi-dimensional dynamics
  • Multi-layered tori
  • Forced period-doubling systems

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