You are in the accessibility menu

Please use this identifier to cite or link to this item: http://acervodigital.unesp.br/handle/11449/7115
Title: 
Time-periodic perturbation of a Lienard equation with an unbounded homoclinic loop
Author(s): 
Institution: 
Universidade Estadual Paulista (UNESP)
ISSN: 
0167-2789
Sponsorship: 
  • Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
  • Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
  • Pró-Reitoria de Pesquisa da UNESP (PROPe UNESP)
Sponsorship Process Number: 
CNPq: 305204/2009-2
Abstract: 
We consider a quadratic Lienard equation with an unbounded homoclinic loop, which is a solution tending in forward and backward time to a non-hyperbolic equilibrium point located at infinity. Under small time-periodic perturbation, this equilibrium becomes a normally hyperbolic line of singularities at infinity. We show that the perturbed system may present homoclinic bifurcations, leading to the existence of transverse intersections between the stable and unstable manifolds of such a normally hyperbolic line of singularities. The global study concerning the infinity is performed using the Poincare compactification in polar coordinates, from which we obtain a system defined on a set equivalent to a solid torus in R(3), whose boundary plays the role of the infinity. The transversality of the manifolds is proved using the Melnikov method and implies, via the Birkhoff-Smale Theorem, a complex dynamical behaviour of the perturbed system solutions in the finite part of the phase space. Numerical simulations are performed in order to illustrate this behaviour, which could be called "the chaos arising from infinity", since it depends on the global structure of the Lienard equation, including the points at infinity. Although applied to a particular case, the analysis presented provides a geometrical approach to study periodic perturbations of homoclinic (or heteroclinic) loops to infinity of any planar polynomial vector field. (C) 2011 Elsevier B.V. All rights reserved.
Issue Date: 
15-Aug-2011
Citation: 
Physica D-nonlinear Phenomena. Amsterdam: Elsevier B.V., v. 240, n. 17, p. 1402-1409, 2011.
Time Duration: 
1402-1409
Publisher: 
Elsevier B.V.
Keywords: 
  • Forced Lienard equation
  • Poincare compactification
  • Melnikov method
  • Homoclinic bifurcation
  • Chaotic dynamics
Source: 
http://dx.doi.org/10.1016/j.physd.2011.06.006
URI: 
Access Rights: 
Acesso restrito
Type: 
outro
Source:
http://repositorio.unesp.br/handle/11449/7115
Appears in Collections:Artigos, TCCs, Teses e Dissertações da Unesp

There are no files associated with this item.
 

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.