Global dynamics of a family of 3D Lotka-Volterra Systems

In this paper we analyze the flow of a family of three dimensional Lotka-Volterra systems restricted to an invariant and bounded region. The behaviour of the flow in the interior of this region is simple: either every orbit is a periodic orbit or they move from one boundary to another. Nevertheless the complete study of the limit sets in the boundary allows to understand the bifurcations which take place in the region as a global bifurcation that we denote by focus--center--focus bifurcation.