Barnabas Garay and Josef Hofbauer:

Robust permanence for ecological differential equations, minimax, and discretizations

SIAM J. Math. Anal. 34 (2003) 1007-1039.

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 (JDE 2000) sufficient condition in terms of Liapunov exponents and give various generalizations. Then we study robustness of permanence criteria against discretizations, with fixed and variable stepsizes. Applications to mathematical ecology and evolutionary games are given.

ps-file (original version July 2001, 55 pp)

reprint (final and shortened version, July 2002)