A singular perturbation method for saddle connections and subharmonics of certain nonlinear differential equations with fixed saddle points.

@article{Smith1990,
abstract = {Saddle connections and subharmonics are investigated for a class of forced second order differential equations which have a fixed saddle point. In these equations, which have linear damping and a nonlinear restoring term, the amplitude of the forcing term depends on displacement in the system. Saddle connections are significant in nonlinear systems since their appearance signals a homoclinic bifurcation. The approach uses a singular perturbation method which has a fairly broad application to saddle connections and also to various subharmonics. The singular perturbation is unusual in that it uses a time-scale which has to be constructed over an infinite interval. The system with a cubic restoring term and a quadratic amplitude is looked at in some detail.},
author = {Smith, Peter},
journal = {Revista Matemática de la Universidad Complutense de Madrid},
keywords = {Ecuaciones diferenciales no lineales; Perturbaciones; Saddle connections; subharmonics; singular perturbation method; Melnikov's method},
language = {eng},
number = {1},
pages = {89-107},
title = {A singular perturbation method for saddle connections and subharmonics of certain nonlinear differential equations with fixed saddle points.},
url = {http://eudml.org/doc/43727},
volume = {3},
year = {1990},
}

TY - JOUR
AU - Smith, Peter
TI - A singular perturbation method for saddle connections and subharmonics of certain nonlinear differential equations with fixed saddle points.
JO - Revista Matemática de la Universidad Complutense de Madrid
PY - 1990
VL - 3
IS - 1
SP - 89
EP - 107
AB - Saddle connections and subharmonics are investigated for a class of forced second order differential equations which have a fixed saddle point. In these equations, which have linear damping and a nonlinear restoring term, the amplitude of the forcing term depends on displacement in the system. Saddle connections are significant in nonlinear systems since their appearance signals a homoclinic bifurcation. The approach uses a singular perturbation method which has a fairly broad application to saddle connections and also to various subharmonics. The singular perturbation is unusual in that it uses a time-scale which has to be constructed over an infinite interval. The system with a cubic restoring term and a quadratic amplitude is looked at in some detail.
LA - eng
KW - Ecuaciones diferenciales no lineales; Perturbaciones; Saddle connections; subharmonics; singular perturbation method; Melnikov's method
UR - http://eudml.org/doc/43727
ER -