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Global stability and repulsion in autonomous Kolmogorov systems

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  • Criteria are established for the global attraction, or global repulsion on a compact invariant set, of interior and boundary fixed points of Kolmogorov systems. In particular, the notions of diagonal stability and Split Lyapunov stability that have found wide success for Lotka-Volterra systems are extended for Kolmogorov systems. Several examples from theoretical ecology and evolutionary game theory are discussed to illustrate the results.
    Mathematics Subject Classification: Primary: 37B25; Secondary: 37C70, 34D23, 34D05.


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