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Hou, Zhanyuan and Baigent, Stephen (2015) Global stability and repulsion in autonomous Kolmogorov systems. Communications on Pure and Applied Analysis, 14 (3). pp. 1205-1238. ISSN 1534-0392
Abstract
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.
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