Permanence in polymatrix replicators

Abstract

Generally a biological system is said to be permanent if under small perturbations none of the species goes to extinction. In 1979 P. Schuster, K. Sigmund, and R. Wolff [14] introduced the concept of permanence as a stability notion for systems that models the self-organization of biological macromolecules. After, in 1987 W. Jansen [8], and J. Hofbauer and K. Sigmund [5] give sufficient conditions for permanence in the usual replicators. In this paper we extend these results for polymatrix replicators.