Results 1 to 10 of about 45,565 (194)
Invariant measures and random attractors of stochastic delay differential equations in Hilbert space
Electronic Journal of Qualitative Theory of Differential Equations, 2022 This paper is devoted to a general stochastic delay differential equation with infinite-dimensional diffusions in a Hilbert space. We not only investigate the existence of invariant measures with either Wiener process or Lévy jump process, but also ...
Shangzhi Li, Shangjiang Guo
doaj +2 more sources
Random attractor for second-order stochastic delay lattice sine-Gordon equation
Boundary Value Problems, 2021 In this paper, we prove the existence of random D $\mathcal{D}$ -attractor for the second-order stochastic delay sine-Gordon equation on infinite lattice with certain dissipative conditions, and then establish the upper bound of Kolmogorov ε-entropy for ...
Xintao Li, Lianbing She, Zhenpei Shan
doaj +1 more source
Exponential attractors for random dynamical systems and applications [PDF]
, 2012 The paper is devoted to constructing a random exponential attractor for some classes of stochastic PDE's. We first prove the existence of an exponential attractor for abstract random dynamical systems and study its dependence on a parameter and then ...
Shirikyan, Armen, Zelik, Sergey
core +2 more sources
Asymptotic behaviour of random Markov chains with tridiagonal generators [PDF]
, 2012 Continuous-time discrete-state random Markov chains generated by a random linear differential equation with a random tridiagonal matrix are shown to have a random attractor consisting of singleton subsets, essentially a random path, in the simplex of ...
Allen +9 more
core +1 more source
Dynamics of the stochastic wave equations with degenerate memory effects on bounded domain [PDF]
Surveys in Mathematics and its Applications, 2022 In this work, we consider the behavior of long-time dynamics of a random dynamical system generated wave equations with degenerate memory and additive noise, on bounded domain U, with Dirichlet boundary condition, and nonlinear term f(u) with critical ...
Abdelmajid A. D. +3 more
doaj
On attractors, spectra and bifurcations of random dynamical systems [PDF]
, 2015 In this thesis a number of related topics in random dynamical systems theory are studied: local attractors and attractor-repeller pairs, the exponential dichotomy spectrum and bifurcation theory.
Callaway, Mark
core +1 more source
AIMS Mathematics, 2021 We study the dynamical behavior of the solutions of stochastic discrete long wave-short wave resonance equations driven by fractional Brownian motions with Hurst parameter $ H\in(\frac{1}{2}, 1) $. And then we prove that the random dynamical system has a
Ranran Liu, Hui Liu, Jie Xin
doaj +1 more source
Random attractors for stochastic evolution equations driven by fractional Brownian motion [PDF]
, 2013 The main goal of this article is to prove the existence of a random attractor for a stochastic evolution equation driven by a fractional Brownian motion with $H\in (1/2,1)$.
Gao, H. +2 more
core +2 more sources
Uniformly Random Attractor for the Three-Dimensional Stochastic Nonautonomous Camassa-Holm Equations
Abstract and Applied Analysis, 2013 We consider the uniformly random attractor for the three-dimensional stochastic nonautonomous Camassa-Holm equations in the periodic box in this paper.
Zhehao Huang, Zhengrong Liu
doaj +1 more source
Entropy, 2020 In this paper, a new 4D hyperchaotic system is generated. The dynamic properties of attractor phase space, local stability, poincare section, periodic attractor, quasi-periodic attractor, chaotic attractor, bifurcation diagram, and Lyapunov index are ...
Lina Ding, Qun Ding
doaj +1 more source