On Random Dynamical Systems Generated by White Noise Time Change of Deterministic Dynamical Systems by Mohamed Hmissi, Farida Mokchaha

“…We prove that the obtained random dynamical systems are solutions of some stochastic differential equations whenever the deterministic dynamical systems are solutions of ordinary differential equations.…”
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H1-Random Attractors and Asymptotic Smoothing Effect of Solutions for Stochastic Boussinesq Equations with Fluctuating Dynamical Boundary Conditions by Yijin Zhang

“…Using a method based on the theory of omega-limit compactness of a random dynamical system, we prove that the L2-random attractor for the generated random dynamical system is exactly the H1-random attractor. …”
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Complexity of a Microblogging Social Network in the Framework of Modern Nonlinear Science by Andrey Dmitriev, Vasily Kornilov, Svetlana Maltseva

“…We offer a new model of a microblogging social network as a nonlinear random dynamical system with additive noise in three-dimensional phase space. …”
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Random Attractors for Stochastic Three-Component Reversible Gray-Scott System with Multiplicative White Noise by Anhui Gu

“…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.…”
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Random Attractors for the Stochastic Discrete Long Wave-Short Wave Resonance Equations by Jie Xin, Hong Lu

“…We prove the asymptotic compactness of the random dynamical system and obtain the random attractor.…”
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A Stochastic Weakly Damped, Forced KdV-BO Equation by Guolian Wang

“…We first show that the global solution generates a random dynamical system. By energy type estimates and dispersive properties, we then prove that this system possesses a weak random attractor in the space H1(ℝ).…”
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Random Attractors for Stochastic Three-Component Reversible Gray-Scott System on Infinite Lattices by Anhui Gu, Zhaojuan Wang, Shengfan Zhou

“…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.…”
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Random Dynamics of the Stochastic Boussinesq Equations Driven by Lévy Noises by Jianhua Huang, Yuhong Li, Jinqiao Duan

“…Some fundamental properties of a subordinator Lévy process and the stochastic integral with respect to a Lévy process are discussed, and then the existence, uniqueness, regularity, and the random dynamical system generated by the stochastic Boussinesq equations are established. …”
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Random Attractors for Stochastic Retarded 2D-Navier-Stokes Equations with Additive Noise by Xiaoyao Jia, Xiaoquan Ding

“…Then conjugation relation between two random dynamical systems implies the existence of a random attractor for the stochastic equation. …”
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Dynamics of Stochastic Coral Reefs Model with Multiplicative Nonlinear Noise by Zaitang Huang

“…Little seems to be known about the ergodicity of random dynamical systems with multiplicative nonlinear noise. …”
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