Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Asymptotic behaviour of a logistic lattice system

Pages: 4019 - 4037, Volume 34, Issue 10, October 2014      doi:10.3934/dcds.2014.34.4019

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Tomás Caraballo - Dpto. Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, Campus Reina Mercedes, Apdo. de Correos 1160, 41080 Sevilla, Spain (email)
Francisco Morillas - Department d'Economia Aplicada, Facultat d'Economia, Universitat de València, Campus del Tarongers s/n, 46022-València, Spain (email)
José Valero - Centro de Investigación Operativa, Universidad Miguel Hernández de Elche, Avda. de la Universidad, s/n, 03202 Elche, Spain (email)

Abstract: In this paper we study the asymptotic behaviour of solutions of a lattice dynamical system of a logistic type. Namely, we study a system of infinite ordinary differential equations which can be obtained after the spatial discretization of a logistic equation with diffusion. We prove that a global attractor exists in suitable weighted spaces of sequences.

Keywords:  Lattice dynamical systems, global attractor, logistic equation, ordinary differential equations, population models.
Mathematics Subject Classification:  35B40, 35B41, 35K55, 34G20, 37L30, 37L60.

Received: December 2012;      Revised: February 2013;      Available Online: April 2014.