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

摘要

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