Journal article
Chaos at the border of criticality
Chaos (Woodbury, N.Y.), v 18(3), pp 033105-033105-7
Sep 2008
PMID: 19045443
Featured in Collection : UN Sustainable Development Goals @ Drexel
Abstract
The present paper points out a novel scenario for the formation of chaotic attractors in a class of models of excitable cell membranes near an Andronov-Hopf bifurcation (AHB). The mechanism underlying chaotic dynamics admits a simple and visual description in terms of the families of one-dimensional first-return maps, which are constructed using the combination of asymptotic and numerical techniques. The bifurcation structure of the continuous system (specifically, the proximity to a degenerate AHB) endows the Poincare map with distinct qualitative features such as unimodality and the presence of the boundary layer, where the map is strongly expanding. This structure of the map in turn explains the bifurcation scenarios in the continuous system including chaotic mixed-mode oscillations near the border between the regions of sub- and supercritical AHB. The proposed mechanism yields the statistical properties of the mixed-mode oscillations in this regime. The statistics predicted by the analysis of the Poincare map and those observed in the numerical experiments of the continuous system show a very good agreement.
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Details
- Title
- Chaos at the border of criticality
- Creators
- Georgi S Medvedev - Department of Mathematics, Drexel University, 3141 Chestnut Street, Philadelphia, Pennsylvania 19104, USA. medvedev@drexel.eduYun Yoo
- Publication Details
- Chaos (Woodbury, N.Y.), v 18(3), pp 033105-033105-7
- Publisher
- American Institute of Physics (AIP); United States
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000260027300005
- Scopus ID
- 2-s2.0-54749142027
- Other Identifier
- 991014877768104721
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InCites Highlights
Data related to this publication, from InCites Benchmarking & Analytics tool:
- Web of Science research areas
- Mathematics, Applied
- Physics, Mathematical