DMS Colloquium: Peter E. Kloeden

Speaker: Peter E. Kloeden (Mathematisches Institut; Universitát Tübingen, Germany; kloeden@na.uni-tuebingen.de)

Title: Lattice Difference Equations

Abstract: Lattice difference  equations are essentially difference equations on a Hilbert space of bi-infinite sequences. They are motivated by the discretisation of the spatial variable in  integrodifference equations arising in theoretical ecology. It is shown here that under similar assumptions to those used for such integrodifference equations they have a global attractor, to which the  global attractors of finite dimensional  approximations  converge upper semi continuously.   Corresponding results are also shown for lattice difference equations when only a finite number of interconnection weights are nonzero and when the  interconnection weights themselves vary and converge in an appropriate manner.