Equilibria in some families of Kolmogorov systems. (English) Zbl 1354.34059
Summary: Kolmogorov systems constitute a general model for the dynamics of biological species. In that sense, they are generalizations of the Lotka-Volterra systems. Here, some classical results on existence, uniqueness, and global attraction of local equilibria that hold in Lotka-Volterra systems are generalized to Kolmogorov systems.
MSC:
| 34C05 | Topological structure of integral curves, singular points, limit cycles of ordinary differential equations |
| 34D20 | Stability of solutions to ordinary differential equations |
| 34D23 | Global stability of solutions to ordinary differential equations |
Software:
MathematicaReferences:
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