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March  2007, 19(1): 177-196. doi: 10.3934/dcds.2007.19.177

Numerical and finite delay approximations of attractors for logistic differential-integral equations with infinite delay

Tomás Caraballo 1, , P.E. Kloeden 2, and  Pedro Marín-Rubio 1,

1. 

Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla
2. 

FB Mathematik, Johann Wolfgang Goethe Universität, Postfach 11 19 32, D-60054 Frankfurt a.M.

Received  June 2006 Revised  March 2007 Published  June 2007

The upper semi-continuous convergence of approximate attractors for an infinite delay differential equation of logistic type is proved, first for the associated truncated delay equation with finite delay and then for a numerical scheme applied to the truncated equation.
Keywords: Attractors for delay differential equations, numerical and theoretical approximations of solutions..
Mathematics Subject Classification: Primary: 34D45, 34K28, 34K25, 34K0.
Citation: Tomás Caraballo, P.E. Kloeden, Pedro Marín-Rubio. Numerical and finite delay approximations of attractors for logistic differential-integral equations with infinite delay. Discrete & Continuous Dynamical Systems, 2007, 19 (1) : 177-196. doi: 10.3934/dcds.2007.19.177
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