Results 271 to 280 of about 40,691 (307)
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Controlling the Dynamics of a Random System
1992Random 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.) +1 more
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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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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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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
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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
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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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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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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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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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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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