Globally Stable Kolmogorov Systems

  • Antonio Tineo
  • Manuel Gamez

Abstract

In this paper, we consider a biological community consisting of p competing subcommunities, such that each subcommunity, in isolation, behaves as a cooperative system. Assuming that the Jacobian matrix is "uniformly stable", we prove that our system is globally asymptotically stable. We also prove a result about persistence, if each subcommunity is globally asymptotically stable. Finally, for p = 2, we use a comparison result by H. L. Smith to prove the existence of a coexistence state.
Published
2002-08-01
Section
Articles