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, 2023 Random differential equations are differential equations whose right-hand side con- tains a random noise. In most applications that noise is modelled by a stochastic process of certain properties or a metric dynamical system.
Garaj, Tomáš
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Linearization of Random Dynamical Systems
1995At the end of the last century the French mathematician Henri Poincare laid the foundation for what we call nowadays the qualitative theory of ordinary differential equations. Roughly speaking, this theory is devoted to studying how the qualitative behavior (e.g.
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Transition to chaos for random dynamical systems
Physical Review Letters, 1990Summary: 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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Interface pinning and dynamics in random systems
Physical Review B, 1990A detailed low-temperature treatment of the domain wall or interface pinning by imperfections in disordered systems with discrete symmetry of the order parameter is presented. Crossover behavior as well as analogies between pinning mechanisms in different systems is analyzed. Pinning may arise from random bonds, when the disordering agents do not break
, Nattermann, , Shapir, , Vilfan
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On a Dynamic Theory of Quenched Random System
Communications in Theoretical Physics, 1983A dynamical theory for quenched random system is developed in the framework of CTPGF. In steady states the results obtained coincide with Chose following from the quenched average of the free energy. The order parameter , a matrix in general, becomes an integral part of the second order connected CTPGF.
Zhao-bing SU, Lu YU, Guang-zhao ZHOU
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ON SMALL RANDOM PERTURBATIONS OF DYNAMICAL SYSTEMS
Russian Mathematical Surveys, 1970In 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.
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Autonomous random perturbations of dynamical systems
Russian Mathematical Surveys, 2002Consider 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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1995
This paper was given as a presentation at the Jahrestagung der DMV in Berlin, 1992. It provides an overview of the theory of random dynamical systems (RDS's), and covers in a very short, but precise way the state of the art in the following areas: 1. Metric, topological, and smooth dynamics, 2. RDS: concept, invariant measures, 3. Generation of RDS, 4.
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This paper was given as a presentation at the Jahrestagung der DMV in Berlin, 1992. It provides an overview of the theory of random dynamical systems (RDS's), and covers in a very short, but precise way the state of the art in the following areas: 1. Metric, topological, and smooth dynamics, 2. RDS: concept, invariant measures, 3. Generation of RDS, 4.
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On the effects of random time in dynamical systems
Kybernetes, 2000Analyzes the effects of internal random time in some dynamical systems. Assumes that this relative time is equal to the absolute time disturbed by an additive random term in the form of a Gaussian white noise, and it is shown that, as a result of the special properties of Brownian motion, it is recommended to use Taylor expansions up to the second ...
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Topological Dynamics of Random Dynamical Systems
1997Abstract This book is devoted to the theory of topological dynamics of random dynamical systems. The theory of random dynamical systems is a relatively new and fast expanding field of research which attracts the attention of researchers from various fields of science. It unites and develops the classical deterministic theory of dynamical
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