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Chaotic behaviour in a singularly perturbed system

Bosch Vivanco, Ignacio (2006) Chaotic behaviour in a singularly perturbed system. Nonlinearity, 19 (7). pp. 1535-1551. ISSN 0951-7715

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Official URL: http://0-iopscience.iop.org.cisne.sim.ucm.es/0951-7715/

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Abstract

The aim of this paper is to present a novel type of chaos observed in a four dimensional singularly perturbed system. The chaotic behavior is described both numerically and analytically. We show the existence of a new
type of strange attractor reminiscent of a chaotic behavior for a fast-slow system. Related to this we demonstrate that there is an invariant attracting region overlapping the jump manifolds of the fast system. This canonical problem was identi¯ed to be a coupled problem of two Hopf bifurcations with
the fast jump process. We derive a geometric model where we can rigorously
show the existence of chaotic orbits.

Item Type:Article
Uncontrolled Keywords:Heteroclinic Cycles; Homoclinic Cycles; Convection; Symmetry
Subjects:Sciences > Mathematics > Differential equations
ID Code:12860
Deposited On:16 Jun 2011 07:12
Last Modified:06 Feb 2014 09:34

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