Random periodic solutions of random dynamical systems

By Huaizhong Zhao, Zuohuan Zheng. 2009

101 citations recorded by the source corpus.

Abstract In this paper, we give the definition of the random periodic solutions of random dynamical systems. We prove the existence of such periodic solutions for a C 1 perfect cocycle on a cylinder using a random invariant set, the Lyapunov exponents and the pullback of the cocycle.

Subfields: Control and Systems Engineering, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/51609e1fecb32865657d35d4755aed87b74e16f7

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Control and Systems Engineering

1. Chunrong Feng
2. Yue Wu
3. Huaizhong Zhao
4. Bixiang Wang
5. Michael Ghil
6. Boya Zhou
7. Mickaël D. Chekroun
8. Eric Simonnet

In Geometry and Topology

1. Chunrong Feng
2. Bixiang Wang
3. Yue Wu
4. Huaizhong Zhao

In Mathematical Physics

1. Chunrong Feng
2. Yue Wu
3. Bixiang Wang
4. Michael Ghil
5. Huaizhong Zhao
6. Mickaël D. Chekroun
7. Eric Simonnet

Citations in the corpus

• Pathwise Random Periodic Solutions of Stochastic Differential Equations (2011, background): “H. Z. Zhao, Z. H. Zheng, Random periodic solutions of random dynamical systems, Journal of Differential Equations, Vol. 246 (2009), 2020-2038.”
• Anticipating Random Periodic Solutions--I. SDEs with Multiplicative Linear Noise (2015, methodology): “If the stochastic system is dissipative, we can use other methods such as pull-back to study the problem, where there is no anticipating issue at all ([33]).”
• Random periodic solutions of SPDEs via integral equations and Wiener-Sobolev compact embedding (2012, methodology): “H. Z. Zhao, Z. H. Zheng, Random periodic solutions of random dynamical systems.”
• Existence, Stability and Bifurcation of Random Complete and Periodic Solutions of Stochastic Parabolic Equations (2013, background): “Note that such a mapping ξ is used in [53] for the definition of random periodic solutions.”
• Attractors of non-autonomous stochastic lattice systems in weighted spaces (2014, unknown): “Such solutions were studied in [61].”
• Random periodic processes, periodic measures and ergodicity (2014, background): “This then led to the rigorous definition of random periodic solutions ([22],[23],[35],[54]).”
• Stochastic climate dynamics: Random attractors and time-dependent invariant measures (2011, background): “, a random periodic orbit [50] that pullback attracts the phase space’s Lebesgue measure.”