Random Attractors for Von Karman Plates Subjected to Multiplicative White Noise Loadings

2016 ◽  
pp. 59-70
Author(s):  
Huatao Chen ◽  
Dengqing Cao ◽  
Jingfei Jiang
Keyword(s):  
White Noise ◽  
Von Karman ◽  
Random Attractors ◽  
Multiplicative White Noise ◽  
Von Kármán

scholarly journals Long Time Behavior and Global Dynamics of Simplified Von Karman Plate Without Rotational Inertia Driven by White Noise

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 315 ◽  
Author(s):  
Huatao Chen ◽  
Dengqing Cao ◽  
Jingfei Jiang ◽  
Xiaoming Fan
Keyword(s):  
White Noise ◽  
External Force ◽  
Dynamical Behavior ◽  
Rotational Inertia ◽  
Global Dynamics ◽  
Time Behavior ◽  
Von Karman ◽  
Random Attractors ◽  
Von Kármán Plate ◽  
Von Kármán

Without the assumption that the coefficient of weak damping is large enough, the existence of the global random attractors for simplified Von Karman plate without rotational inertia driven by either additive white noise or multiplicative white noise are proved. Instead of the classical splitting method, the techniques to verify the asymptotic compactness rely on stabilization estimation of the system. Furthermore, a clear relationship between in-plane components of the external force that act on the edge of the plate and the expectation of radius of the global random attractors can be obtained from the theoretical results. Based on the relationship between global random attractor and random probability invariant measure, the global dynamics of the plates are analyzed numerically. With increasing the in-plane components of the external force that act on the edge of the plate, global D-bifurcation, secondary global D-bifurcation and complex local dynamical behavior occur in motion of the system. Moreover, increasing the intensity of white noise leads to the dynamical behavior becoming simple. The results on global dynamics reveal that random snap-through which seems to be a complex dynamics intuitively is essentially a simple dynamical behavior.

scholarly journals Random Attractors for Stochastic Three-Component Reversible Gray-Scott System on Infinite Lattices

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Anhui Gu ◽  
Zhaojuan Wang ◽  
Shengfan Zhou
Keyword(s):  
Dynamical System ◽  
White Noise ◽  
Random Attractor ◽  
Random Dynamical System ◽  
Random Attractors ◽  
Multiplicative White Noise ◽  
Infinite Lattices

We prove the existence of a compact random attractor for the random dynamical system generated by stochastic three-component reversible Gray-Scott system with a multiplicative white noise on infinite lattices.

scholarly journals Random attractors for stochastic retarded reaction-diffusion equations with multiplicative white noise on unbounded domains

2018 ◽  
Vol 16 (1) ◽  
pp. 862-884
Author(s):  
Xiaoyao Jia ◽  
Xiaoquan Ding ◽  
Juanjuan Gao
Keyword(s):  
Dynamical Systems ◽  
White Noise ◽  
Reaction Diffusion ◽  
Random Parameter ◽  
Reaction Diffusion Equations ◽  
Random Dynamical Systems ◽  
Diffusion Equations ◽  
Uhlenbeck Process ◽  
Random Attractors ◽  
Multiplicative White Noise

AbstractIn this paper we investigate the stochastic retarded reaction-diffusion equations with multiplicative white noise on unbounded domain ℝn (n ≥ 2). We first transform the retarded reaction-diffusion equations into the deterministic reaction-diffusion equations with random parameter by Ornstein-Uhlenbeck process. Next, we show the original equations generate the random dynamical systems, and prove the existence of random attractors by conjugation relation between two random dynamical systems. In this process, we use the cut-off technique to obtain the pullback asymptotic compactness.

scholarly journals Existence and Upper Semicontinuity of Attractors for Nonautonomous Stochastic Sine-Gordon Lattice Systems with Random Coupled Coefficients

2016 ◽  
Vol 2016 ◽  
pp. 1-12
Author(s):  
Zhaojuan Wang ◽  
Shengfan Zhou
Keyword(s):  
White Noise ◽  
Weighted Space ◽  
Upper Semicontinuity ◽  
Lattice Systems ◽  
Random Attractors ◽  
Multiplicative White Noise

We study nonautonomous stochastic sine-Gordon lattice systems with random coupled coefficients and multiplicative white noise. We first consider the existence of random attractors in a weighted space for this system and then establish the upper semicontinuity of random attractors as the intensity of noise approaches zero.

scholarly journals Random Attractors for Stochastic Three-Component Reversible Gray-Scott System with Multiplicative White Noise

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Anhui Gu
Keyword(s):  
Dynamical System ◽  
White Noise ◽  
Random Attractor ◽  
Random Dynamical System ◽  
Random Attractors ◽  
Multiplicative White Noise

The paper is devoted to proving the existence of a compact random attractor for the random dynamical system generated by stochastic three-component reversible Gray-Scott system with multiplicative white noise.

scholarly journals Random attractors for stochastic lattice dynamical systems with infinite multiplicative white noise

2016 ◽  
Vol 130 ◽  
pp. 255-278 ◽  
Author(s):  
Tomás Caraballo ◽  
Xiaoying Han ◽  
Björn Schmalfuss ◽  
José Valero
Keyword(s):  
Dynamical Systems ◽  
White Noise ◽  
Random Attractors ◽  
Multiplicative White Noise ◽  
Lattice Dynamical Systems

scholarly journals Regularity of Wong-Zakai approximation for non-autonomous stochastic quasi-linear parabolic equation on $ {\mathbb{R}}^N $

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Guifen Liu ◽  
Wenqiang Zhao
Keyword(s):  
Differential Equation ◽  
Parabolic Equation ◽  
White Noise ◽  
Parabolic Equations ◽  
Growth Exponent ◽  
Linear Parabolic Equation ◽  
Approximation Technique ◽  
Linear Parabolic Equations ◽  
Random Attractors ◽  
Multiplicative White Noise

<p style='text-indent:20px;'>In this paper, we investigate a non-autonomous stochastic quasi-linear parabolic equation driven by multiplicative white noise by a Wong-Zakai approximation technique. The convergence of the solutions of quasi-linear parabolic equations driven by a family of processes with stationary increment to that of stochastic differential equation with white noise is obtained in the topology of <inline-formula><tex-math id="M2">\begin{document}$ L^2( {\mathbb{R}}^N) $\end{document}</tex-math></inline-formula> space. We establish the Wong-Zakai approximations of solutions in <inline-formula><tex-math id="M3">\begin{document}$ L^l( {\mathbb{R}}^N) $\end{document}</tex-math></inline-formula> for arbitrary <inline-formula><tex-math id="M4">\begin{document}$ l\geq q $\end{document}</tex-math></inline-formula> in the sense of upper semi-continuity of their random attractors, where <inline-formula><tex-math id="M5">\begin{document}$ q $\end{document}</tex-math></inline-formula> is the growth exponent of the nonlinearity. The <inline-formula><tex-math id="M6">\begin{document}$ L^l $\end{document}</tex-math></inline-formula>-pre-compactness of attractors is proved by using the truncation estimate in <inline-formula><tex-math id="M7">\begin{document}$ L^q $\end{document}</tex-math></inline-formula> and the higher-order bound of solutions.</p>

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