ON THE ASYMPTOTIC BEHAVIOR OF A CLASS OF DETERMINISTIC MODELS OF COOPERATING SPECIES.

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Abstract

In this paper the global behavior of solutions of a class of ordinary differential equations modeling n cooperating biological species is determined. The class of systems includes the classical Lotka-Volterra systems as well as more realistic and more highly nonlinear systems. The fundamental tools are the Kamke theorem, results of M. W. Hirsch for so-called cooperative systems and the Perron-Frobenius theory of nonnegative matrices and its extensions.

Original languageEnglish (US)
Pages (from-to)368-375
Number of pages8
JournalSIAM Journal on Applied Mathematics
Volume46
Issue number3
DOIs
StatePublished - Jan 1 1986

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ASJC Scopus subject areas

  • Applied Mathematics

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