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Zbl 1111.34027
Gyllenberg, Mats; Yan, Ping; Wang, Yi
Limit cycles for competitor-competitor-mutualist Lotka-Volterra systems. (English)
[J] Physica D 221, No. 2, 135-145 (2006). ISSN 0167-2789

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.
[Angela Slavova (Sofia)]

MSC 2000:: *34C05 Qualitative theory of some special solutions of ODE
34C60 Applications of qualitative theory of ODE
37N25 Dynamical systems in biology

Keywords: Lotka-Volterra systems; limit cycles; periodic orbits

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