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Pré-Publication, Document De Travail Année : 2017

Global asymptotic stability of coexistence steady-states in integro-differential Lotka-Volterra systems

Résumé

We analyse the asymptotic behaviour of integro-differential equations modelling N populations in interaction, where interactions are modelled by non-local terms involving linear combinations of the total number of individuals in each population. This model generalises the usual Lotka-Volterra ordinary differential equations. Our aim is to give conditions under which there is global asymptotical stability of coexistence steady-states at the level of the total number of individuals in each species. Through the analysis of a Lyapunov function, our first main result gives a simple and general condition on the matrix of interactions, together with a convergence rate. The second main result establishes another type of condition in the specific case of mutualistic interactions. These conditions are compared to the well-known condition given by Goh for classical Lotka-Volterra ordinary differential equations.
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Dates et versions

hal-01470722 , version 1 (17-02-2017)
hal-01470722 , version 2 (22-03-2017)
hal-01470722 , version 3 (23-03-2017)
hal-01470722 , version 4 (14-04-2017)

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Camille Pouchol, Emmanuel Trélat. Global asymptotic stability of coexistence steady-states in integro-differential Lotka-Volterra systems. 2017. ⟨hal-01470722v1⟩
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