ATTRACTORS FOR STOCHASTIC LATTICE DYNAMICAL SYSTEMS

By Peter W. Bates, Hannelore Lisei, Kening Lu. 2006

281 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8782c87c15c9a1d89a1a65de8cb743e9dd31f1de

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Citations in the corpus

Asymptotic behavior of random fitzhugh-nagumo systems driven by colored noise (2017, background): “The concept of random attractors was introduced in [18, 21, 44] and further studied in [6, 7, 8, 9, 11, 12, 13, 15, 16, 18, 22, 23, 24, 26, 32, 37, 40, 50, 51] for the autonomous stochastic equations; and in [2, 14, 19, 27, 28, 52, 53, 54] for the non-autonomous stochastic equations.”
Asymptotic Behavior of Stochastic Wave Equations with Critical Exponents on R^3 (2008, background): “The following existence result on a random attractor for a continuous RDS can be found in [6, 19].”
Non--autonomous and random attractors for delay random semilinear equations without uniqueness (2008, background): “[4] where asymptotically compact single valued systems are studied.”
Existence and continuity of bi-spatial random attractors and application to stochastic semilinear Laplacian equations (2015, background): “This concept generalizes some common concepts of random attractors (see [8,14,15,17]) and tempered random attractors (see [3–5,7,30,31,34]).”
On differential equations with delay in Banach spaces and attractors for retarded lattice dynamical systems (2013, unknown): “, [6], [11], [12] [13], [26], [27], [35], [49], [46]).”
Invariant measures of stochastic delay lattice systems (2021, background): “The random dynamics of stochastic lattice equations have been recently examined in [5, 6, 14, 15, 32, 33, 35, 61, 62] and the references therein.”
Random attractors for stochastic reaction–diffusion equations on unbounded domains (2009, background): “The following existence result for a random attractor for a continuous RDS can be found in [8,17].”
Random attractors for stochastic sine-Gordon lattice systems with multiplicative white noise (2011, background): “(See [2,12].”
Upper semicontinuity of random attractors for non-compact random dynamical systems. (2009, methodology): “re dist(·,·) is the Hausdorﬀ semi-metric given by dist(Y,Z) = sup y∈Y inf z∈Z ky−zkX for any Y ⊆ X and Z⊆ X. The following existence result for a random attractor for a continuous RDS can be found in [3, 4, 13]. 4 Proposition 2.8. Let D be an inclusion-closed collection of random subsets of X and φa”
Asymptotic behavior of stochastic wave equations with critical exponents on $\mathbb{R}^{3}$ (2008, background): “The following existence result on a random attractor for a continuous RDS can be found in [6, 19].”
Limiting Behavior of Invariant Measures of Stochastic Delay Lattice Systems (2021, background): “There is an enormous number of publications on the solutions and their long-term dynamics for lattice systems, which, for instance, can be found in [1–3,7,16,21,27,30,39] for deterministic lattice systems and in [4,5,11,22,31,34,37] for stochastic lattice systems.”
Sufficient and Necessary Criteria for Existence of Pullback Attractors for Non-compact Random Dynamical Systems (2012, background): “The compactness of Φ was later replaced by the D-pullback asymptotic compactness and the existence of attractors in this case was proved in [5].”
Attractors of non-autonomous stochastic lattice systems in weighted spaces (2014, background): “The existence of random attractors for autonomous stochastic lattice systems was first proved in [7], followed by extensions in [17, 18, 38, 39, 48] and the references therein.”