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 m. We investigate the topological structure of this system as m varies along the entire real line R. As we shall see there are five distinct cases for all m 2 R. A bifurcation scenario occurs at m 1⁄4 0 and m 1⁄4 2, respectively. Our study partly recovers the results known in Mcgehee (1981). 2014 Elsevier Inc. All rights reserved.