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Stochastic Synchronization of Random Pullback Attractors

2020
In this and in the next chapter we deal with the synchronization of random dynamical systems (RDS). The concept of RDS (see Arnold [4] and the literature cited therein) covers the most important families of dynamical systems with randomness, including random and stochastic ordinary and partial differential equations and random difference equations ...
Igor Chueshov, Björn Schmalfuß
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Random attractors of boussinesq equations with multiplicative noise

Acta Mathematica Sinica, English Series, 2009
Consider Stratonovich-interpreted two-dimensional Boussinesq equation perturbed by multiplicative white noise \[ dv + [(v \cdot \nabla) v - \nu \Delta v + \nabla p] dt = e_2(T-T_1) dt + bv \circ dW(t) \] \[ dT+[(v \cdot \nabla)T-\kappa \Delta T)] dt = 0 \] \[ \mathrm{div}(v) = 0 \] on the domain \(D = (0,1)^2\), where \(e_i\) are the unit vectors of \(\
Li, Yangrong, Guo, Boling
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Measure attractors and random attractors for stochastic partial differential equations

Stochastic Analysis and Applications, 1999
In the theory of stochastic differential equations we can distinguish between two kinds of attractors. The first one is the attractor (measure attractor) with respect to the Markov semigroup generated by a stochastic differential equation. The second meaning of attractors (random attractors) is to be understood with respect to each trajectory of the ...
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Multifractal properties of snapshot attractors of random maps

Physical Review A, 1990
We consider qualitative and quantitative properties of ``snapshot attractors'' of random maps. By a random map we mean that the parameters that occur in the map vary randomly from iteration to iteration according to some probability distribution. By a ``snapshot attractor'' we mean the measure resulting from many iterations of a cloud of initial ...
, Romeiras, , Grebogi, , Ott
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Random Walk on a Strange Attractor

Physical Review Letters, 1984
On etudie les proprietes de transport des attracteurs etranges a l'aide d'une marche de sauterelle a sauts aleatoire sur des points separes d'une distance a±sa sur l ...
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Random attractors for initial memory codes

Proceedings of International Conference on Neural Networks (ICNN'97), 2002
The problem of how the temporal relations among events are converted to the spatial structure in neural connections are considered. Random coding is one hypothesis to this problem, in which items to be stored are associated with randomly chosen network attractors, independent of spatial relationships between the items.
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Random attractors for asymptotically upper semicompact multivalue random semiflows

Applied Mathematics and Mechanics, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Random Exponential Attractor for the 3D Non-autonomous Stochastic Damped Navier–Stokes Equation

Journal of Dynamics and Differential Equations, 2021
Zongfei Han, Shengfan Zhou
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