2 citations · 3 across the 6 of their papers we have counts for
6 papers
Center manifolds for infinite dimensional random dynamical systems
Xiaopeng Chen, Anthony J. Roberts, Jinqiao Duan
Stochastic center manifolds theory are crucial in modelling the dynamical behavior of complex systems under stochastic influences. A multiplicative ergodic theorem on Hilbert space…
Center manifolds for stochastic evolution equations
Xiaopeng Chen, A. J. Roberts, Jinqiao Duan
Stochastic invariant manifolds are crucial in modelling the dynamical behavior of dynamical systems under uncertainty. Under the assumption of exponential trichotomy, existence and…
Evolution systems of measures for stochastic flows
Xiaopeng Chen, Jinqiao Duan, Michael Scheutzow
A new concept of {\em an evolution system of measures for stochastic flows} is considered. It corresponds to the notion of an invariant measure for random dynamical systems (or coc…
A sufficient condition for bifurcation in random dynamical systems
Xiaopeng Chen, Jinqiao Duan, Xinchu Fu
Some properties of random Conley index are obtained and then a sufficient condition for the existence of abstract bifurcation points for both discrete-time and continuous-time rand…
State space decomposition for nonautonomous dynamical systems
Xiaopeng Chen, Jinqiao Duan
Decomposition of state spaces into dynamically different components is helpful for the understanding of dynamical behaviors of complex systems. A Conley type decomposition theorem…
Random Chain Recurrent Sets for Random Dynamical Systems
Xiaopeng Chen, Jinqiao Duan
It is known by the Conley's theorem that the chain recurrent set of a deterministic flow on a compact metric space is the complement of the union of sets , wher…