Synchronization by noise for order-preserving random dynamical systems

  title={Synchronization by noise for order-preserving random dynamical systems},
  author={F. Flandoli and B. Gess and M. Scheutzow},
  journal={arXiv: Probability},
  • F. Flandoli, B. Gess, M. Scheutzow
  • Published 2015
  • Mathematics
  • arXiv: Probability
  • We provide sufficient conditions for weak synchronization by noise for order-preserving random dynamical systems on Polish spaces. That is, under these conditions we prove the existence of a weak point attractor consisting of a single random point. This generalizes previous results in two directions: First, we do not restrict to Banach spaces and second, we do not require the partial order to be admissible nor normal. As a second main result and application we prove weak synchronization by… CONTINUE READING
    23 Citations
    • 4
    • PDF
    Synchronization by noise
    • 42
    • PDF
    Additive noise destroys the random attractor close to bifurcation
    • 7
    • PDF
    Noise-induced strong stabilization
    Couplings via comparison principle and exponential ergodicity of SPDEs in the hypoelliptic setting
    • 5
    • PDF


    Synchronization by noise
    • 42
    • PDF
    Order-preserving random dynamical systems: equilibria, attractors, applications
    • 75
    On the structure of attractors and invariant measures for a class of monotone random systems
    • 62
    The Global Random Attractor for a Class of Stochastic Porous Media Equations
    • 40
    • PDF
    Random Attractors for Degenerate Stochastic Partial Differential Equations
    • 47
    • PDF
    Attractors for random dynamical systems
    • 732
    Stabilization of Stationary Solutions of Evolution Equations by Noise
    • 6
    • Highly Influential