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Title: Richness of dynamics and global bifurcations in systems with a homoclinic figure-eight
Author: Gonchenko, Sergey V.
Simó, Carles
Vieiro Yanes, Arturo
Keywords: Teoria de la bifurcació
Teoria ergòdica
Sistemes dinàmics de baixa dimensió
Bifurcation theory
Ergodic theory
Low-dimensional dynamical systems
Issue Date: 17-Jan-2013
Publisher: IOP Publishing
Abstract: We consider 2D flows with a homoclinic figure-eight to a dissipative saddle. We study the rich dynamics that such a system exhibits under a periodic forcing. First, we derive the bifurcation diagram using topological techniques. In particular, there is a homoclinic zone in the parameter space with a non-smooth boundary. We provide a complete explanation of this phenomenon relating it to primary quadratic homoclinic tangency curves which end up at some cubic tangency (cusp) points. We also describe the possible attractors that exist (and may coexist) in the system. A main goal of this work is to show how the previous qualitative description can be complemented with quantitative global information. To this end, we introduce a return map model which can be seen as the simplest one which is 'universal' in some sense. We carry out several numerical experiments on the model, to check that all the objects predicted to exist by the theory are found in the model, and also to investigate new properties of the system.
Note: Versió postprint del document publicat a:
It is part of: Nonlinearity, 2013, vol. 26, num. 3, p. 621-678
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ISSN: 0951-7715
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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