TITLE:
Homoclinic Bifurcation of a Quadratic Family of Real Functions with Two Parameters
AUTHORS:
Salma M. Farris, Karam N. Abdul-Kareem
KEYWORDS:
Local Unstable Set, Unstable Set, Homoclinic Point, Homoclinic Orbit, Non-Degenerate, Homoclinic Tangency, Homoclinic Bifurcation
JOURNAL NAME:
Open Access Library Journal,
Vol.8 No.5,
May
31,
2021
ABSTRACT: In this work the homoclinic bifurcation of the family H={h(a,b)(x)=ax2+b:a∈R/{0},b∈R}
is studied. We proved that this family has a homoclinic tangency associated to x=0 of P1 for b=-2/a. Also we proved that Wu(P1) does not intersect the backward orbit of P1 for b>-2/a, but has intersection for b0. So H has this type of the bifurcation.