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Gradient Infinite-Dimensional Random Dynamical Systems [PDF]

SIAM Journal on Applied Dynamical Systems, 2012
In this paper we introduce the concept of a gradient random dynamical system as a random semiflow possessing a continuous random Lyapunov function which describes the asymptotic regime of the system.
Tomáš Caraballo, JOSÉ A Langa, Zhenxin Liu   +2 more
exaly   +2 more sources

A Siegel theorem for dynamical systems under random perturbations

Discrete and Continuous Dynamical Systems - Series B, 2008
In this paper, we generalize the classical Siegel's theorem for deterministic dynamical systems to that under random perturbations.Mathematics, AppliedSCI(E)0ARTICLE3-4635 ...
Kening Lu, Weigu Li
exaly   +2 more sources

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Dynamical Spectrum in Random Dynamical Systems

Journal of Dynamics and Differential Equations, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Guangwa, Cao, Yongluo
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Conley index for random dynamical systems

Journal of Differential Equations, 2008
Conley index theory is a very powerful tool in the study of dynamical systems. In this paper, we generalize Conley index theory to discrete random dynamical systems. Our constructions are basically the random version of Franks and Richeson in [J. Franks,
Zhenxin Liu
exaly   +2 more sources

Controlling the Dynamics of a Random System

1992
Random systems, dynamical systems and control systems can all be described as flows on (finite or infinite dimensional) spaces, which allows for the use of unified concepts in the analysis of their qualitative long term behavior. In particular there is a close connection between the attractors of an undisturbed system, the stationary and ergodic ...
Colonius, Fritz (Prof.), Kliemann, Wolfgang   +1 more
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Random Dynamical Systems

2007
This treatment provides an exposition of discrete time dynamic processes evolving over an infinite horizon. Chapter 1 reviews some mathematical results from the theory of deterministic dynamical systems, with particular emphasis on applications to economics. The theory of irreducible Markov processes, especially Markov chains, is surveyed in Chapter 2.
Rabi Bhattacharya, Mukul Majumdar
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Random Dynamical Systems

2016
In this chapter we will introduce methods and techniques to analyze models with stochasticity or randomness. In particular we will establish the framework of random dynamical systems and introduce the concept of random attractors.
Tomás Caraballo, Xiaoying Han
openaire   +1 more source

Transition to chaos for random dynamical systems

Physical Review Letters, 1990
Summary: We study the transition to chaos for random dynamical systems. Near the transition, on the chaotic side, the long-time particle distribution (which is fractal) that evolves from an initial smooth distribution exhibits an extreme form of temporally intermittent bursting whose scaling we investigate.
Yu, Lei, Ott, Edward, Chen, Qi
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Autonomous random perturbations of dynamical systems

Russian Mathematical Surveys, 2002
Consider an oscillation with one degree of freedom perturbed by a small friction \[ \ddot q_t^{\varepsilon} + f(q_t^{\varepsilon}) = -\varepsilon \dot q_t^{\varepsilon}, \qquad 0< \varepsilon \ll 1. \] This equation is a special case of the Hamiltonian system \[ \dot X_t^{\varepsilon}=\bar\nabla H(X_t^{\varepsilon}) +\varepsilon b(X_t^{\varepsilon ...
Freidlin, M., Ren, Huaizhong
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ON SMALL RANDOM PERTURBATIONS OF DYNAMICAL SYSTEMS

Russian Mathematical Surveys, 1970
In this paper we study the effect on a dynamical system of small random perturbations of the type of white noise: where is the -dimensional Wiener process and as . We are mainly concerned with the effect of these perturbations on long time-intervals that increase with the decreasing .
Ventcel', A. D., Freidlin, M. I.
openaire   +2 more sources