Bosch Vivanco, Ignacio (2006) Chaotic behaviour in a singularly perturbed system. Nonlinearity, 19 (7). pp. 1535-1551. ISSN 0951-7715
Official URL: http://0-iopscience.iop.org.cisne.sim.ucm.es/0951-7715/
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.
|Uncontrolled Keywords:||Heteroclinic Cycles; Homoclinic Cycles; Convection; Symmetry|
|Subjects:||Sciences > Mathematics > Differential equations|
|Deposited On:||16 Jun 2011 09:12|
|Last Modified:||16 Jun 2011 09:12|
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