An extremum principle for parabolic competition

Zoltán Varga, Eörs Szathmáry

Research output: Contribution to journalArticle

11 Citations (Scopus)


Parabolic growth invariably results in the survival of all competing types. Under the constraint of constant total concentration, there is a unique equilibrium in the simplex interior, which is asymptotically stable inside the whole simplex. The appropriate Lyapunov function is obtained in terms of the excess productivity which is shown to be maximized for the competitive system with fractional order kinetics. Claims to the contrary are refuted.

Original languageEnglish
Pages (from-to)1145-1154
Number of pages10
JournalBulletin of Mathematical Biology
Issue number6
Publication statusPublished - Nov 1997

ASJC Scopus subject areas

  • Neuroscience(all)
  • Immunology
  • Mathematics(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Environmental Science(all)
  • Pharmacology
  • Agricultural and Biological Sciences(all)
  • Computational Theory and Mathematics

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