, Volume 10, Issue 1, pp 51-64,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 09 Feb 2011

Invariant Torus in 3D Lotka–Volterra Systems Appearing After Perturbation of Hopf Center

Abstract

We study a three dimensional Lotka–Volterra systems. In the paper Bobieński and Żołądek (J Ergod Theory Dyn Syst 25:759–791, 2005) four cases of center (i.e. an invariant surface supporting a center) were found. In this paper, we study a codimension 2 component LV Hopf and its versal deformation. We prove that at most one invariant torus may appear. This invariant torus corresponds to the limit cycle bifurcating in the amplitude system.

Supported by Polish KBN Grant No 2 P03A 015 29.