The Jungle Universe: coupled cosmological models in a Lotka–Volterra framework

Jérôme Perez 1 André Füzfa 2 Timoteo Carletti 3 Laurence Mélot Laurent Guedezounme
1 OC - Optimisation et commande
2 naXys
3 Department of Mathematics
Abstract : In this paper, we exploit the fact that the dynamics of homogeneous and isotropic Friedmann-Lemaitre universes is a special case of generalized Lotka-Volterra system where the competitive species are the barotropic fluids filling the Universe. Without coupling between those fluids, Lotka-Volterra formulation offers a pedagogical and simple way to interpret usual Friedmann-Lemaitre cosmological dynamics. A natural and physical coupling between cosmological fluids is proposed which preserve the structure of the dynamical equations. Using the standard tools of Lotka-Volterra dynamics, we obtain the general Lyapunov function of the system when one of the fluids is coupled to dark energy. This provides in a rigorous form a generic asymptotic behavior for cosmic expansion in presence of coupled species, beyond the standard de Sitter, Einstein-de Sitter and Milne cosmologies. Finally, we conjecture that chaos can appear for at least four interacting fluids.
Keywords : Cosmology · Coupled models · Dynamical systems · Dark energy · Predator-prey system
Type de document :
Article dans une revue
General Relativity and Gravitation, Springer Verlag, 2014, 46, pp.1753. 〈10.1007/s10714-014-1753-8〉
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https://hal-ensta.archives-ouvertes.fr/hal-00968772
Contributeur : Aurélien Arnoux <>
Soumis le : mardi 1 avril 2014 - 15:09:34
Dernière modification le : mercredi 6 décembre 2017 - 16:46:01

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Jérôme Perez, André Füzfa, Timoteo Carletti, Laurence Mélot, Laurent Guedezounme. The Jungle Universe: coupled cosmological models in a Lotka–Volterra framework. General Relativity and Gravitation, Springer Verlag, 2014, 46, pp.1753. 〈10.1007/s10714-014-1753-8〉. 〈hal-00968772〉

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