Bifurcations of a non-gravitational interaction problem

This paper studies a particular planar problem which can be related to the interaction of two bodies under the action of a non-gravitational force field. Specifically, the mathematical description of this problem is a system of ordinary differential equations depending on a parameter ν. We investigate the topological structure of this system as ν varies along the entire real line R. As we shall see there are five distinct cases for all ν∈R. A bifurcation scenario occurs at ν=0 and ν=2, respectively. Our study partly recovers the results known in Mcgehee (1981).