Pullback and forward attractors for dissipative lattice dynamical systems with additive noises

Jung Chao Ban, Cheng Hsiung Hsu, Yin Heng Lin, Tzi Sheng Yang

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

This work investigates the dissipative dynamical system in the infinite lattice . The dynamics of each node depends on itself and nearby nodes by a nonlinear function. When each node is perturbed with weighted Gaussian white noise, a unique pullback attractor and forward attractor exists whose domain of attraction are random tempered sets. Furthermore, we prove that the pullback and forward attractors are equivalent to a random equilibrium which is also tempered. Both convergence to the pullback and forward attractors are exponentially fast.

Original languageEnglish
Pages (from-to)139-155
Number of pages17
JournalDynamical Systems
Volume24
Issue number2
DOIs
StatePublished - Jun 2009

Keywords

  • Pullback and forward attractors
  • Tempered random equilibrium

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