Facultative Mutualisms and θ -Logistic Growth: How Larger Exponents Promote Global Stability of Co-Existence Equilibria

Paul Georgescu () and Hong Zhang
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Paul Georgescu: Department of Mathematics, Technical University of Iaşi, Bd. Copou 11, 700506 Iaşi, Romania
Hong Zhang: School of Economics and Management, Changzhou Institute of Technology, Changzhou 213032, China

Mathematics, 2023, vol. 11, issue 20, 1-19

Abstract: We investigate the stability of co-existence equilibria for two-species models of facultative mutualism for which birth and death are modeled as separate processes, with possibly distinct types of density dependence, and the mutualistic contributions are either linear or saturating. To provide a unifying perspective, we first introduce and discuss a generic stability framework, finding sufficient stability conditions expressed in terms of reproductive numbers computed at high population densities. To this purpose, an approach based on the theory of monotone dynamical systems is employed. The outcomes of the generic stability framework are then used to characterize the dynamics of the two-species models of concern, delineating between decelerating (lower-powered) and accelerating (higher-powered) density dependences. It is subsequently seen that accelerating density dependences promote the stability of co-existence equilibria, while decelerating density dependences either completely destabilize the system via promoting the unboundedness of solutions or create multiple co-existence equilibria.

Keywords: mutualistic interactions; global stability of co-existence equilibria; boundedness framework; monotone dynamical systems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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