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Limit cycles for competitor-competitor-mutualist Lotka-Volterra systems. (English) Zbl 1111.34027

Here, a competitor-competitor-mutualist Lotka-Volterra system is studied. The authors prove that the number of periodic orbits for such system is finite. New conditions on the coefficients are derived in order the system not to have nontrivial periodic orbits. In this way, it is proved that the positive equilibrium is globally asymptotically stable. Several examples are provided as well.

MSC:

34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34C60 Qualitative investigation and simulation of ordinary differential equation models
37N25 Dynamical systems in biology
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