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

Jérome Perez; André Füzfa; Timoteo Carletti; Laurence Melot; Sêcloka Lazare Guedezounme

doi:10.1007/s10714-014-1753-8

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

Jérome Perez, André Füzfa, Timoteo Carletti, Laurence Melot, Sêcloka Lazare Guedezounme

Résultats de recherche: Contribution à un journal/une revue › Article › Revue par des pairs

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Résumé

In this paper, we exploit the fact that the dynamics of homogeneous and
isotropic Friedmann–Lemaître 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–Lemaître cosmological
dynamics. A natural and physical coupling between cosmological fluids is proposed
which preserves 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.

langue originale	Anglais
Numéro d'article	46
Pages (de - à)	1753
Nombre de pages	23
journal	General Relativity and Gravitation
Volume	46
Numéro de publication	4
Les DOIs	https://doi.org/10.1007/s10714-014-1753-8
Etat de la publication	Publié - 1 mai 2014

mots-clés

dynamical systems, cosmology, population dynamics

Accès au document

10.1007/s10714-014-1753-8

GenRelGrav_46_2014pp1753Version finale publiée, 672 KB

http://link.springer.com/article/10.1007%2Fs10714-014-1753-8

PAI n°P7/19 - DYSCO: Dynamical systems, control and optimization (DYSCO)
Winkin, J. (Co-investigateur), Blondel, V. (Responsable du Projet), Vandewalle, J. (Co-investigateur), Pintelon, R. M. (Co-investigateur), Sepulchre, R. (Co-investigateur), Vande Wouwer, A. (Co-investigateur) & Sartenaer, A. (Co-investigateur)
1/04/12 → 30/09/17
Projet: Recherche
ARCCOS - ARC11/15-040: The Interplay between dark energy and primordial inflation
Fuzfa, A. (Responsable du Projet) & Ringeval, C. (Co-investigateur)
1/09/11 → 31/08/15
Projet: Recherche

The Jungle Universe
Melot, L. (Auteur)Fuzfa, A. (Promoteur) & Pérez, J. (Copromoteur), 30 juin 2012
Student thesis: Master types › Master en sciences mathématiques

Contient cette citation

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title = "The Jungle Universe: coupled cosmological models in a Lotka–Volterra framework",

abstract = "In this paper, we exploit the fact that the dynamics of homogeneous andisotropic Friedmann–Lema{\^i}tre universes is a special case of generalized Lotka–Volterra system where the competitive species are the barotropic fluids filling theUniverse. Without coupling between those fluids, Lotka–Volterra formulation offersa pedagogical and simple way to interpret usual Friedmann–Lema{\^i}tre cosmologicaldynamics. A natural and physical coupling between cosmological fluids is proposedwhich preserves the structure of the dynamical equations. Using the standard toolsof Lotka–Volterra dynamics, we obtain the general Lyapunov function of the systemwhen one of the fluids is coupled to dark energy. This provides in a rigorous forma generic asymptotic behavior for cosmic expansion in presence of coupled species,beyond the standard de Sitter, Einstein-de Sitter and Milne cosmologies. Finally, weconjecture that chaos can appear for at least four interacting fluids.",

keywords = "Cosmology, Coupled models, Dynamical systems, Dark energy, Predator-prey system, dynamical systems, cosmology, population dynamics",

author = "J{\'e}rome Perez and Andr{\'e} F{\"u}zfa and Timoteo Carletti and Laurence Melot and Guedezounme, {S{\^e}cloka Lazare}",

year = "2014",

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AU - Perez, Jérome

AU - Füzfa, André

AU - Carletti, Timoteo

AU - Melot, Laurence

AU - Guedezounme, Sêcloka Lazare

PY - 2014/5/1

Y1 - 2014/5/1

N2 - In this paper, we exploit the fact that the dynamics of homogeneous andisotropic Friedmann–Lemaître universes is a special case of generalized Lotka–Volterra system where the competitive species are the barotropic fluids filling theUniverse. Without coupling between those fluids, Lotka–Volterra formulation offersa pedagogical and simple way to interpret usual Friedmann–Lemaître cosmologicaldynamics. A natural and physical coupling between cosmological fluids is proposedwhich preserves the structure of the dynamical equations. Using the standard toolsof Lotka–Volterra dynamics, we obtain the general Lyapunov function of the systemwhen one of the fluids is coupled to dark energy. This provides in a rigorous forma generic asymptotic behavior for cosmic expansion in presence of coupled species,beyond the standard de Sitter, Einstein-de Sitter and Milne cosmologies. Finally, weconjecture that chaos can appear for at least four interacting fluids.

AB - In this paper, we exploit the fact that the dynamics of homogeneous andisotropic Friedmann–Lemaître universes is a special case of generalized Lotka–Volterra system where the competitive species are the barotropic fluids filling theUniverse. Without coupling between those fluids, Lotka–Volterra formulation offersa pedagogical and simple way to interpret usual Friedmann–Lemaître cosmologicaldynamics. A natural and physical coupling between cosmological fluids is proposedwhich preserves the structure of the dynamical equations. Using the standard toolsof Lotka–Volterra dynamics, we obtain the general Lyapunov function of the systemwhen one of the fluids is coupled to dark energy. This provides in a rigorous forma generic asymptotic behavior for cosmic expansion in presence of coupled species,beyond the standard de Sitter, Einstein-de Sitter and Milne cosmologies. Finally, weconjecture that chaos can appear for at least four interacting fluids.

KW - Cosmology

KW - Coupled models

KW - Dynamical systems

KW - Dark energy

KW - Predator-prey system

KW - dynamical systems, cosmology, population dynamics

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DO - 10.1007/s10714-014-1753-8

M3 - Article

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JF - General Relativity and Gravitation

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

Résumé

mots-clés

Accès au document

Empreinte digitale

Projets

PAI n°P7/19 - DYSCO: Dynamical systems, control and optimization (DYSCO)

ARCCOS - ARC11/15-040: The Interplay between dark energy and primordial inflation

Thèses de l'étudiant

The Jungle Universe

Contient cette citation