Asymptotic behavior of stochastic Schrödinger lattice systems driven by nonlinear noise

2019 ◽  
Vol 38 (2) ◽  
pp. 213-237
Author(s):  
Bixiang Wang ◽  
Renhai Wang
Keyword(s):  
Asymptotic Behavior ◽  
Lattice Systems ◽  
Nonlinear Noise

scholarly journals Asymptotic behavior of non-autonomous fractional stochastic lattice systems with multiplicative noise

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yiju Chen ◽  
Xiaohu Wang
Keyword(s):  
Asymptotic Behavior ◽  
Multiplicative Noise ◽  
Upper Semicontinuity ◽  
Random Attractor ◽  
Discrete Laplacian ◽  
Lattice Systems ◽  
Random Attractors ◽  
Infinite Range Interactions ◽  
Infinite Range

<p style='text-indent:20px;'>In this paper, we study the asymptotic behavior of non-autonomous fractional stochastic lattice systems with multiplicative noise. The considered systems are driven by the fractional discrete Laplacian, which features the infinite-range interactions. We first prove the existence of pullback random attractor in <inline-formula><tex-math id="M1">\begin{document}$ \ell^2 $\end{document}</tex-math></inline-formula> for stochastic lattice systems. The upper semicontinuity of random attractors is also established when the intensity of noise approaches zero.</p>

scholarly journals Asymptotic Behavior of Stochastic Partly Dissipative Lattice Systems in Weighted Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-23
Author(s):  
Xiaoying Han
Keyword(s):  
Dynamical System ◽  
Asymptotic Behavior ◽  
Weighted Space ◽  
Random Dynamical System ◽  
Absorbing Set ◽  
Lattice Systems ◽  
Lattice Differential Equations ◽  
Additive White Noise ◽  
Bounded Absorbing Set ◽  
Infinite Sequences

We study stochastic partly dissipative lattice systems with random coupled coefficients and multiplicative/additive white noise in a weighted space of infinite sequences. We first show that these stochastic partly dissipative lattice differential equations generate a random dynamical system. We then establish the existence of a tempered random bounded absorbing set and a global compact random attractor for the associated random dynamical system.

scholarly journals Long Term Behavior for a Class of Stochastic Delay Lattice Systems in Xρ Space

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Yijin Zhang ◽  
Zongbing Lin
Keyword(s):  
Dynamical System ◽  
Asymptotic Behavior ◽  
Existence And Uniqueness ◽  
Additive Noise ◽  
Asymptotic Behavior Of Solutions ◽  
Random Dynamical System ◽  
Lattice Systems ◽  
Stochastic Delay ◽  
Long Term Behavior

In this paper, we focus on the asymptotic behavior of solutions to stochastic delay lattice equations with additive noise and deterministic forcing. We first show the existence of a continuous random dynamical system for the equations. Then we investigate the pullback asymptotical compactness of solutions as well as the existence and uniqueness of tempered random attractor in Xρ space. Finally, ergodicity of the systems is achieved.

scholarly journals Dynamics of Stochastic Coral Reefs Model with Multiplicative Nonlinear Noise

2016 ◽  
Vol 2016 ◽  
pp. 1-15
Author(s):  
Zaitang Huang
Keyword(s):  
Asymptotic Behavior ◽  
Dynamical Systems ◽  
Probability Measure ◽  
Coral Reefs ◽  
Stationary Distribution ◽  
Markov Semigroup ◽  
Support Theorem ◽  
Stationary Density ◽  
Behavior Dynamics ◽  
Nonlinear Noise

Little seems to be known about the ergodicity of random dynamical systems with multiplicative nonlinear noise. This paper is devoted to discern asymptotic behavior dynamics through the stochastic coral reefs model with multiplicative nonlinear noise. By support theorem and Hörmander theorem, the Markov semigroup corresponding to the solutions is to prove the Foguel alternative. Based on boundary distributions theory, the required conservative operators related to the solutions are further established to ensure the existence a stationary distribution. Meanwhile, the density of the distribution of the solutions either converges to a stationary density or weakly converges to some probability measure.

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