RANDOM PULLBACK ATTRACTOR FOR A NON-AUTONOMOUS MODIFIED SWIFT-HOHENBERG EQUATION WITH MULTIPLICATIVE NOISE

In this paper, we study the existence of the random -pullback attractor of a non-autonomous local modiﬁed stochastic Swift-Hohenberg equation with multiplicative noise in stratonovich sense. It is shown that a random -pullback attractor exists in when its external force has exponential growth. Due to the stochastic term, the estimate are delicate, we overcome this difficulty by using the Ornstein-Uhlenbeck(O-U) transformation and its properties.

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Random pullback attractor of a non-autonomous local modified stochastic Swift–Hohenberg equation with multiplicative noise

Journal of Mathematical Physics ◽

10.1063/5.0008895 ◽

2020 ◽

Vol 61 (9) ◽

pp. 092703

Author(s):

Yongjun Li ◽

Hongqing Wu ◽

Tinggang Zhao

Keyword(s):

Multiplicative Noise ◽

Pullback Attractor

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Random attractors for stochastic two-compartment Gray-Scott equations with a multiplicative noise

Open Mathematics ◽

10.1515/math-2016-0052 ◽

2016 ◽

Vol 14 (1) ◽

pp. 586-602 ◽

Cited By ~ 1

Author(s):

Xiaoyao Jia ◽

Juanjuan Gao ◽

Xiaoquan Ding

Keyword(s):

Dynamical System ◽

Neumann Boundary Condition ◽

Multiplicative Noise ◽

Space Dimension ◽

Stochastic Equation ◽

Uniform Estimate ◽

Neumann Boundary ◽

Random Dynamical System ◽

Pullback Attractor ◽

Homogeneous Neumann Boundary Condition

Abstract In this paper, we consider the existence of a pullback attractor for the random dynamical system generated by stochastic two-compartment Gray-Scott equation for a multiplicative noise with the homogeneous Neumann boundary condition on a bounded domain of space dimension n ≤ 3. We first show that the stochastic Gray-Scott equation generates a random dynamical system by transforming this stochastic equation into a random one. We also show that the existence of a random attractor for the stochastic equation follows from the conjugation relation between systems. Then, we prove pullback asymptotical compactness of solutions through the uniform estimate on the solutions. Finally, we obtain the existence of a pullback attractor.

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Iteratively Reweighted Anisotropic-TV Based Multiplicative Noise Removal Model

ACTA AUTOMATICA SINICA ◽

10.3724/sp.j.1004.2012.00444 ◽

2012 ◽

Vol 38 (3) ◽

pp. 444-451 ◽

Cited By ~ 4

Author(s):

Xu-Dong WANG ◽

Xiang-Chu FENG ◽

Lei-Gang HUO

Keyword(s):

Multiplicative Noise ◽

Noise Removal ◽

Multiplicative Noise Removal ◽

Removal Model

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Analysis of Stochastic Generation and Shifts of Phantom Attractors in a Climate–Vegetation Dynamical Model

Mathematics ◽

10.3390/math9121329 ◽

2021 ◽

Vol 9 (12) ◽

pp. 1329

Author(s):

Lev Ryashko ◽

Dmitri V. Alexandrov ◽

Irina Bashkirtseva

Keyword(s):

Multiplicative Noise ◽

Nonlinear Dynamical Systems ◽

Stochastic Theory ◽

Slow Variable ◽

Theoretical Description ◽

Mathematical Study ◽

Stochastic Generation ◽

Nonlinear Dynamical ◽

Additive And Multiplicative Noise ◽

And Shifts

A problem of the noise-induced generation and shifts of phantom attractors in nonlinear dynamical systems is considered. On the basis of the model describing interaction of the climate and vegetation we study the probabilistic mechanisms of noise-induced systematic shifts in global temperature both upward (“warming”) and downward (“freezing”). These shifts are associated with changes in the area of Earth covered by vegetation. The mathematical study of these noise-induced phenomena is performed within the framework of the stochastic theory of phantom attractors in slow-fast systems. We give a theoretical description of stochastic generation and shifts of phantom attractors based on the method of freezing a slow variable and averaging a fast one. The probabilistic mechanisms of oppositely directed shifts caused by additive and multiplicative noise are discussed.

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