On the structure of attractors and invariant measures for a class of monotone random systems

By Igor D. Chueshov, M. Scheutzow. 2004

90 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/f17c2afe3efcae7f664ab245c696a4b27a9739a1

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In Computational Theory and Mathematics

In Control and Systems Engineering

In Molecular Biology

Bixiang Wang

Citations in the corpus

Asymptotic Behavior of Stochastic Wave Equations with Critical Exponents on R^3 (2008, background): “The random attractors of stochastic partial differential equations defined in bounded domains have been extensively investigated by many authors in [9, 10, 12, 13, 14, 19, 23, 41] and the references therein.”
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 $\mathbb{R}^{3}$ (2008, background): “The random attractors of stochastic partial differential equations defined in bounded domains have been extensively investigated by many authors in [9, 10, 12, 13, 14, 19, 23, 41] and the references therein.”
Pullback attractors of non-autonomous stochastic degenerate parabolic equations on unbounded domains (2013, background): “Since then, such attractors for autonomous stochastic PDEs have been studied in [6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 30, 31] in bounded domains, and in [4, 33, 34] in unbounded domains.”
Fractal dimension of a random invariant set (2006, unknown): “For the equation: du = ( u + βu − u3)dt + εφ dWt with u|∂U = 0, on a bounded domain U ⊂ R with φ ∈ D(A) (for d 4), the analysis in Debussche paper show that df(A) cβd/2, an estimate of the same order as in the deterministic c However, we note here that it has recently been shown that in fact the ran”
Sufficient and Necessary Criteria for Existence of Pullback Attractors for Non-compact Random Dynamical Systems (2012, background): “The concept of pullback attractors for random dynamical systems was introduced by the authors in [16, 18, 24], and the existence of such attractors for compact systems was established in [1, 7, 8, 14, 15, 16, 17, 18, 21, 22, 24] and the references therein.”
Existence, Stability and Bifurcation of Random Complete and Periodic Solutions of Stochastic Parabolic Equations (2013, background): “ role of complete solutions should be replaced by stationary solutions, and in this case, random attractors are bounded by extremal stationary solutions from above and below, respectively, see, e.g., [1, 16, 17]. Note that the articles mentioned above deal with either deterministic systems or autono”
Attractors of non-autonomous stochastic lattice systems in weighted spaces (2014, background): “, [25, 26, 40, 47, 53].”