Quantitative analysis of competition models
Chiralt, Cristina (Universitat Jaume I. Departament de Matemàtiques)
Ferragut Amengual, Antoni Manel (Universitat Jaume I. Departament de Matemàtiques)
Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Vindel, Pura (Universitat Jaume I. Departament de Matemàtiques)

Date:	2017
Abstract:	We study a 2-species Lotka-Volterra type differential system, modeling competition between two species and having a coexistence equilibrium in the first quadrant. In case that this equilibrium is of saddle type, its stable manifold divides the first quadrant into two zones. Then, depending on the zone where the initial condition lies, one of the species will extinct and the other will go to an equilibrium. Using this separatrix we introduce a measure to discern which species has more chance of surviving. This measure is given by a non-negative real number~ that we will call persistence ratio, that only depends on the parameters of the system. In some cases, we can give simple explicit expressions for . When this is not possible, we use several dynamical tools to obtain effective approximations of~it.
Grants:	Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 Ministerio de Economía y Competitividad MTM2013-40998-P Ministerio de Economía y Competitividad MTM2014-52016-C02-2-P Ministerio de Economía y Competitividad MTM2016-77278-P
Note:	Agraïments: C. Chiralt, A. Ferragut and P. Vindel are partially supported by the Universitat Jaume I grant P1-1B2015-16. P. Vindel is partially supported by the Universitat Politècnica de València grant PROMETEO/2016/089.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Algebraic approximation ; Invariant algebraic curves ; Lotka-Volterra differential system ; Separatrix
Published in:	Nonlinear Analysis: Real World Applications, Vol. 38 (2017) , p. 327-347, ISSN 1468-1218

DOI: 10.1016/j.nonrwa.2017.06.001

Postprint 21 p, 1.9 MB

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