A 3D competitive Lotka-Volterra system with three limit cycles: a falsification of a conjecture by Hofbauer and So. (English) Zbl 1085.34025
In three-dimensional competitive Lotka-Volterra systems, contrary to the two-dimensional case, limit cycles may occur. So far, examples with two limit cycles have been found. Moreover, one example with a heteroclinic polycycle has been shown to possess even three limit cycles. In this paper, the authors construct an explicit three-dimensional competitive Lotka-Volterra system without a heteroclinic polycycle that also exhibits three limit cycles. The procedure of this construction is very artificial and technical.
Reviewer: Josef Hainzl (Freiburg)
MSC:
| 34C05 | Topological structure of integral curves, singular points, limit cycles of ordinary differential equations |
| 92D25 | Population dynamics (general) |
| 34C23 | Bifurcation theory for ordinary differential equations |
| 34C37 | Homoclinic and heteroclinic solutions to ordinary differential equations |
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