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

Smith, Peter. "A singular perturbation method for saddle connections and subharmonics of certain nonlinear differential equations with fixed saddle points.." Revista Matemática de la Universidad Complutense de Madrid 3.1 (1990): 89-107. <http://eudml.org/doc/43727>.

@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 -