On the global flow of a 3--dimensional Lotka--Volterra system
Alavez-Ramírez, Justino (UJAT(México). División Académica de Ciencias Básicas)
Blé, Gamaliel (UJAT(México). División Académica de Ciencias Básicas)
Castellanos, Víctor (UJAT(México). División Académica de Ciencias Básicas)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2012
Abstract:	In the study of the black holes with Higgs field appears in a natural way the Lotka-Volterra differential system x˙= x(y − 1), y˙= y(1 + y − 2x2 − z2), z˙= zy, in R3. Here we provide the qualitative analysis of the flow of this system describing the α-limit set and the ω-limit set of all orbits of this system in the whole Poincar'e ball, i. e. we identify R3 with the interior of the unit ball of R3 centered at the origin and we extend analytically this flow to its boundary, i. e. to the infinity.
Grants:	Ministerio de Ciencia y Tecnología MTM2005-06098-C02-01 Agència de Gestió d'Ajuts Universitaris i de Recerca 2005/SGR-550
Note:	Agraïments: The first author is partially supported by the grant PROMEP/103.5/08/3189. The first three authors are partially supported by two CONACYT grants with numbers 58968 and 62613.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	α-limit ; ω-limit ; Phase portrait ; Lotka-Volterra system ; Black hole ; Higgs field
Published in:	Nonlinear Analysis : Theory, Methods and Applications, Vol. 75 (2012) , p. 4114-4125, ISSN 0362-546X

DOI: 10.1016/j.na.2012.03.002

Postprint 19 p, 407.9 KB

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