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

Murza, Adrian C. ; Teruel, Antonio E.
Dynamical Systems 25, 269-284 (2010)

In this paper we analyse the flow of a family of three dimensional Lotka-Volterra systems restricted to an invariant and bounded region. We conclude that the behaviour of the flow in the interior of this region is very simple: either every orbit is a periodic orbit or they move from one boundary to another. We also characterise some of the bifurcations taking place at the boundary of the invariant region.