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 b<-2/a with a>0. So H has this type of the bifurcation.
Cite this paper
Farris, S. M. and Abdul-Kareem, K. N. (2021). Homoclinic Bifurcation of a Quadratic Family of Real Functions with Two Parameters. Open Access Library Journal, 8, e7300. doi: http://dx.doi.org/10.4236/oalib.1107300.
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Abdul-Kareem, K.N. and Farris, S.M. (2020) Homoclinic Points and Homoclinic Orbits for the Quadratic Family of Real Functions with Two Parameters. Open Access Library Journal, 7, 1-18. https://doi.org/10.4236/oalib.1106170
Abdul-Kareem, K.N. and Farris, S.M. (2020) Homoclinic Points and Bifurcation for a Quadratic Family with Two Parameters. MSc Thesis, Department of Mathematics, College of Computer and Mathematical Sciences, University of Mosul, Mosul, Iraq, 1-98.
