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 language | English |
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Pages (from-to) | 139-155 |
Number of pages | 17 |
Journal | Dynamical Systems |
Volume | 24 |
Issue number | 2 |
DOIs | |
State | Published - Jun 2009 |
Keywords
- Pullback and forward attractors
- Tempered random equilibrium