Threshold boundedness conditions for n-species mutualisms

Document Type

Article

Publication Date

11-9-2017

Journal Title

Nonlinearity

Volume

30

Issue

12

Abstract

We establish boundedness results for a model of mutualism with an arbitrary number of species which encompasses several classic two-species models, even when extended to their respective multidimensional versions. These conditions are obtained under fairly general assumptions on the mathematical form of the functions modelling the mutualistic interactions and are expressed in terms of reproductive ratios at high population densities introduced ad hoc. We then discuss particular cases in which there is a single threshold parameter separating boundedness from unboundedness. The situation in which the unboundedness is caused by a particular subset of species is also of concern.

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