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May  2008, 9(3&4, May): 581-593. doi: 10.3934/dcdsb.2008.9.581

Equi-Attraction and the continuous dependence of attractors on time delays

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

1. 

FB Mathematik, Johann Wolfgang Goethe Universität, Postfach 11 19 32, D-60054 Frankfurt a.M.
2. 

Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080–Sevilla, Spain

Received  September 2006 Revised  January 2007 Published  February 2008

Under appropriate regularity conditions it is shown that the continuous dependence of the global attractors $\mathcal{A}_\tau$ of semi dynamical systems $S^{(\tau)}(t)$ in $C([-\tau,0];Z)$ with $Z$ a Banach space and time delay $\tau \in [T_*,T^$*$]$, where $T_* > 0$, is equivalent to the equi-attraction of the attractors. Examples and counter examples posed in this right framework are provided.
Keywords: extended semiflows and attractors, parametric attractors, continuity of attractors and equi-attraction., Semiflows for delay differential equations.
Mathematics Subject Classification: Primary: 34D45, 37C70, 34K2.
Citation: P.E. Kloeden, Pedro Marín-Rubio. Equi-Attraction and the continuous dependence of attractors on time delays. Discrete & Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 581-593. doi: 10.3934/dcdsb.2008.9.581
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