Artículos de revistas
Heteroclinic bifurcations near Hopf-zero bifurcation in reversible vector fields in R-3
Registro en:
Journal Of Differential Equations. Academic Press Inc Elsevier Science, v. 219, n. 1, n. 78, n. 115, 2005.
0022-0396
WOS:000233442500004
10.1016/j.jde.2005.02.019
Autor
Lamb, JSW
Teixeira, MA
Webster, KN
Institución
Resumen
We study the dynamics near a symmetric Hopf-zero (also known as saddle-node Hopf or fold-Hopf) bifurcation in a reversible vector field in R-3, with involutory an reversing symmetry whose fixed point subspace is one-dimensional. We focus on the case in which the normal form for this bifurcation displays a degenerate family of heteroclinics between two asymmetric saddle-foci. We study local perturbations of this degenerate family of heteroclinics within the class of reversible vector fields and establish the generic existence of hyperbolic basic sets (horseshoes), independent of the eigenvalues of the saddle-foci, as well as cascades of bifurcations of periodic, heteroclinic and homoclinic orbits. Finally, we discuss the application of our results to the Michelson system, describing stationary states and travelling waves of the Kuramoto-Sivashinsky PDE. (c) 2005 Elsevier Inc. All rights reserved. 219 1 78 115