Robust Permanence for Ecological Differential Equations, Minimax, and Discretizations

Abstract

We present a sufficient condition for robust permanence of ecological (or Kolmogorov) differential equations based on average Liapunov functions. Via the minimax theorem we rederive Schreiber’s sufficient condition [S. Schreiber, J. Differential Equations, 162 (2000), pp. 400–426] in terms of Liapunov exponents and give various generalizations. Then we study robustness of perma-nence criteria against discretizations with fixed and variable stepsizes. Applications to mathematical ecology and evolutionary games are given.