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Nonlinear Sciences > Chaotic Dynamics

arXiv:nlin/0502012 (nlin)
[Submitted on 7 Feb 2005]

Title:Route to Chaos in Three-Dimensional Maps of Logistic Type

Authors:Daniele Fournier-Prunaret, Ricardo Lopez-Ruiz, Abdel-Kaddous Taha
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Abstract: A route to chaos is studied in 3-dimensional maps of logistic type. Mechanisms of period doubling for invariant closed curves (ICC) are found for specific 3-dimensional maps. These bifurcations cannot be observed for ICC in the 2-dimensional case. When the parameter of the system is modified, localized oscillations occur on the ICC that give rise to weakly chaotic rings, then to chaotic attractors, which finally disappear by contact bifurcations. These maps can be considered as models for the symbiotic interaction of three species.
Comments: 8 pages, 15 figures
Subjects: Chaotic Dynamics (nlin.CD); Dynamical Systems (math.DS); Pattern Formation and Solitons (nlin.PS); Populations and Evolution (q-bio.PE)
Cite as: arXiv:nlin/0502012 [nlin.CD]
  (or arXiv:nlin/0502012v1 [nlin.CD] for this version)
  https://doi.org/10.48550/arXiv.nlin/0502012

Submission history

From: Ricardo Lopez-Ruiz [view email]
[v1] Mon, 7 Feb 2005 10:58:50 UTC (947 KB)
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