A permanence theorem for replicator and Lotka-Volterra systems
The author obtains sufficient conditions for the boundary of a compact invariant set S of the replicator equations to be a repeller and conditions for it not to be a repeller. These conditions are formulated in terms of the existence of an average Lyapunov function in the form of a power function. He then demonstrates how these sufficiency conditions can be checked by solving an equivalent linear programming problem. These results require the compactness of S, but the author also shows how to extend his results to the flow in the positive quadrant determined by Lotka-Volterra equations.
existence of an average Lyapunov function
scientific article; zbMATH DE number 4057352