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Everything about Random dynamical system
Mathematical concept
In mathematics, a random dynamical system is a dynamical system in which the equations of motion have an element of randomness to them. Random dynamical systems are characterized by a state space S, a set of maps from S into itself that can be thought of as the set of all possible equations of motion, and a probability distribution Q on the set that represents the random choice of map. Motion in a random dynamical system can be informally thought of as a state evolving according to a succession of maps randomly chosen according to the distribution Q. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Random dynamical systemA 5-minute orientation
- Skim a recent paper: Random feature models for learning interacting dynamical systemsInfluential work since 2022
- Pick up a classic book: Monte Carlo Simulation in Statistical PhysicsThe most-reprinted book on the subject
- Read the landmark paper: Attractors for random dynamical systemsCited 842 times
- Go sideways: Continuous-time Markov chainA closely related topic
- Go sideways: Flow (mathematics)A closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Attractors for random dynamical systems
Mean-square random dynamical systems
Random periodic solutions of random dynamical systems
Chebyshev polynomial approximation for dynamical response problem of random system
Random dynamical system in time domain: A POD-PC model
Random Conformal Dynamical Systems
RANDOM DYNAMICAL SYSTEMS IN ECONOMICS
Random dynamical systems: a review
🆕 Influential since 2022
Random feature models for learning interacting dynamical systems
Observation-Based Filtering of State of a Nonlinear Dynamical System with Random Delays
Random dynamical system generated by the 3D Navier-Stokes equation with rough transport noise
Robust prediction of chaotic systems with random errors using dynamical system deep learning
Iterated invariance principle for random dynamical systems
📚 Books worth reading
Monte Carlo Simulation in Statistical PhysicsKurt Binder · 2002
Random dynamical systemsRabi Bhattacharya, Mukul Majumdar · 2007
Mirror-image asymmetryJames P. Riehl · 2010
Decision Systems And Nonstochastic RandomnessV. I. Ivanenko · 2010
Monte Carlo simulation in statistical physicsBinder, K. · 1988
Intersections of Random WalksGregory F. Lawler · 1992
Noise-induced phenomena in slow-fast dynamical systemsBerglund, Nils, Barbara Gentz · 2005- 📕Advances in System Dynamics and ControlAhmad Taher Azar, Sundarapandian Vaidyanathan · 2018
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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- Pullback attractor In mathematics, the attractor of a random dynamical system may be loosely thought of as a set to which the system evolves after a long enough time. The…
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