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

Hal Smith

doi:10.1137/0146025

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

Hal Smith

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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 language	English (US)
Pages (from-to)	368-375
Number of pages	8
Journal	SIAM Journal on Applied Mathematics
Volume	46
Issue number	3
DOIs	https://doi.org/10.1137/0146025
State	Published - Jan 1 1986

ASJC Scopus subject areas

Applied Mathematics

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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.",

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AB - 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.

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

Abstract

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