REGULAR DYNAMICS AND BOX-COUNTING DIMENSION FOR A RANDOM REACTION-DIFFUSION EQUATION ON UNBOUNDED DOMAINS

[1]  J. Langa,et al.  Regularity and structure of pullback attractors for reaction–diffusion type systems without uniqueness , 2016 .

[2]  Zhaojuan Wang,et al.  Finite fractal dimension of random attractor for stochastic non-autonomous strongly damped wave equation , 2018, Comput. Math. Appl..

[3]  Feng Zhou,et al.  Continuity and pullback attractors for a non-autonomous reaction-diffusion equation in RN , 2016, Comput. Math. Appl..

[4]  P. Kloeden,et al.  Strong \begin{document}$ (L^2,L^\gamma\cap H_0^1) $\end{document}-continuity in initial data of nonlinear reaction-diffusion equation in any space dimension , 2020, Electronic Research Archive.

[5]  W. Tan,et al.  Non-autonomous reaction–diffusion model with dynamic boundary conditions , 2016 .

[6]  J. Langa,et al.  Measurability of Random Attractors for Quasi Strong-to-Weak Continuous Random Dynamical Systems , 2018 .

[7]  A. Wójcik,et al.  Attractors and asymptotic dynamics of open discrete-time quantum walks on cycles , 2019, Physical Review A.

[8]  Bixiang Wang,et al.  Sufficient and Necessary Criteria for Existence of Pullback Attractors for Non-compact Random Dynamical Systems , 2012, 1202.2390.

[9]  H. Crauel,et al.  Attractors for random dynamical systems , 1994 .

[10]  I. Chueshov.  Monotone Random Systems Theory and Applications , 2002 .

[11]  Continuity of strong solutions of the Reaction–Diffusion equation in initial data , 2008 .

[12]  Yangrong Li,et al.  Existence and continuity of bi-spatial random attractors and application to stochastic semilinear Laplacian equations , 2015 .

[13]  Brian R. Hunt,et al.  Regularity of embeddings of infinite-dimensional fractal sets into finite-dimensional spaces , 1999 .

[14]  Yangrong Li,et al.  A modified proof of pullback attractors in a Sobolev space for stochastic FitzHugh-Nagumo equations , 2016 .

[15]  Heteroclinic chaotic behavior driven by a Brownian motion , 2013 .

[16]  Bixiang Wang.  Existence and Upper Semicontinuity of Attractors for Stochastic Equations with Deterministic Non-autonomous Terms , 2012, 1205.4658.

[17]  Dingshi Li,et al.  Regularity of random attractors for fractional stochastic reaction–diffusion equations onRn , 2018, Journal of Differential Equations.

[18]  Kening Lu,et al.  Chaotic behavior in differential equations driven by a Brownian motion , 2011 .

[19]  B. Schmalfuß,et al.  Bounds on the Hausdorff dimension of random attractors for infinite-dimensional random dynamical systems on fractals , 2019, Discrete & Continuous Dynamical Systems - B.

[20]  Olga Vechtomova,et al.  Stochastic , 2020, Definitions.

[21]  Shengfan Zhou,et al.  Fractal dimension of random attractors for stochastic non-autonomous reaction-diffusion equations , 2016, Appl. Math. Comput..

[22]  Wenqiang Zhao,et al.  Higher-order Wong–Zakai approximations of stochastic reaction–diffusion equations on RN , 2020 .

[23]  Xiaohu Wang,et al.  Wong-Zakai approximations and attractors for stochastic reaction-diffusion equations on unbounded domains , 2018 .

[24]  Boling Guo,et al.  Random attractors for quasi-continuous random dynamical systems and applications to stochastic reaction–diffusion equations☆ , 2008 .

[25]  James C. Robinson,et al.  Fractal dimension of a random invariant set , 2006 .

[26]  Yangrong Li,et al.  Box-counting dimensions and upper semicontinuities of bi-spatial attractors for stochastic degenerate parabolic equations on an unbounded domain , 2017 .

[27]  Joseph L. Shomberg.  Attractors for damped semilinear wave equations with a Robin–acoustic boundary perturbation , 2015, Nonlinear Analysis.

[28]  Shengfan Zhou,et al.  Finite fractal dimensions of random attractors for stochastic FitzHugh–Nagumo system with multiplicative white noise , 2016 .

[29]  Daomin Cao,et al.  Dynamics for a stochastic reaction–diffusion equation with additive noise , 2015 .

[30]  M. Gyllenberg,et al.  Chaotic attractors in the four-dimensional Leslie–Gower competition model , 2020 .

[31]  Chengkui Zhong,et al.  Existence of a global attractor for a p-Laplacian equation in Rn , 2007 .

[32]  Yijin Zhang,et al.  Compactness and attracting of random attractors for non-autonomous stochastic lattice dynamical systems in weighted space , 2016, Appl. Math. Comput..

[33]  L. Arnold.  Random Dynamical Systems , 2003 .

[34]  H. Crauel,et al.  Minimal random attractors , 2017, Journal of Differential Equations.

[35]  K. Lu,et al.  Wong–Zakai Approximations and Long Term Behavior of Stochastic Partial Differential Equations , 2019 .