The global stability of coexisting equilibria for three models of mutualism

Paul Georgescu; Hong  Zhang; Daniel  Maxin

doi:10.3934/mbe.2016.13.101

Article Contents

2016, Volume 13, Issue 1: 101-118. Doi: 10.3934/mbe.2016.13.101

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The global stability of coexisting equilibria for three models of mutualism

1.
Department of Mathematics, Technical University of Iaşi, Bd. Copou 11, 700506 Iaşi
2.
Department of Financial Mathematics, Jiangsu University, ZhenJiang, Jiangsu, 212013

Received: December 31, 2014

Revised: May 31, 2015

Published: September 2015

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Abstract

We analyze the dynamics of three models of mutualism, establishing the global stability of coexisting equilibria by means of Lyapunov's second method. This further establishes the usefulness of certain Lyapunov functionals of an abstract nature introduced in an earlier paper. As a consequence, it is seen that the use of higher order self-limiting terms cures the shortcomings of Lotka-Volterra mutualisms, preventing unbounded growth and promoting global stability.

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Mathematics Subject Classification: Primary: 92D25, 92D40; Secondary: 34D20, 34D23, 93D30.

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