Uniform attractor of the non-autonomous discrete Selkov model

Xiaolin Jia; Caidi Zhao; Juan Cao

doi:10.3934/dcds.2014.34.229

Article Contents

2014, Volume 34, Issue 1: 229-248. Doi: 10.3934/dcds.2014.34.229

This issue Previous Article Pullback attractors for the non-autonomous 2D Navier--Stokes equations for minimally regular forcing Next Article Frequency domain conditions for finite-dimensional projectors and determining observations for the set of amenable solutions

Uniform attractor of the non-autonomous discrete Selkov model

1.
Department of Mathematics and Information Science, Wenzhou University, Zhejiang Province, 325035
2.
College of Teacher Education, Wenzhou University, Zhejiang Province, 325035

Received: October 31, 2012

Revised: February 28, 2013

Published: December 2013

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Abstract

This paper studies the asymptotic behavior of solutions for the non-autonomous lattice Selkov model. We prove the existence of a uniform attractor for the generated family of processes and obtain an upper bound of the Kolmogorov $\varepsilon$-entropy for it. Also we establish the upper semicontinuity of the uniform attractor when the infinite lattice systems are approximated by finite lattice systems.

Keywords:

Non-autonomous lattice dynamical system,
Selkov model,
Uniform attractor,
Kolmogorov $\varepsilon$-entropy,
Upper semicontinuity.

Mathematics Subject Classification: 37L30, 35B40, 35B41.

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