Global stability of the coexistence equilibrium for a general class of models of facultative mutualism

Abstract

Many models of mutualism have been proposed and studied individually. In this paper, we develop a general class of models of facultative mutualism that covers many of such published models. Using mild assumptions on the growth and self-limiting functions, we establish necessary and sufficient conditions on the boundedness of model solutions and prove the global stability of a unique coexistence equilibrium whenever it exists. These results allow for a greater flexibility in the way each mutualist species can be modelled and avoid the need to analyse any single model of mutualism in isolation. Our generalization also allows each of the mutualists to be subject to a weak Allee effect. Moreover, we find that if one of the interacting species is subject to a strong Allee effect, then the mutualism can overcome it and cause a unique coexistence equilibrium to be globally stable.

Threshold boundedness conditions for n-species mutualisms

“…In proving our main result we use boundedness techniques similar to those employed in [18,19]. Consider the mutualism system…”

Mutualism and predator interference: One consumer, two resources

“…Mutualism is an extremely frequent type of interaction in nature. 7 It has been studied through mathematical models since the 1970s; see earlier research [8][9][10] and the references therein. In 1981, Addicot proposed a mutualism model where both species grow logistically.…”