Everything about Dynamical system
Mathematical model of the time dependence of a point in space
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air, and the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured. Time can be measured by integers, by real or complex numbers or can be a more general algebraic object, losing the memory of its physical origin, and the space may be a manifold or simply a set, without the need of a smooth space-time structure defined on it. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Dynamical systemA 5-minute orientation
- Skim a recent paper: Modern Koopman Theory for Dynamical SystemsInfluential work since 2022
- Pick up a classic book: ChaosThe most-reprinted book on the subject
- Read the landmark paper: Numerical integration of the cartesian equations of motion of a system with constraints: molecular dynamics of n-alkanesCited 20,362 times
- Go sideways: Ergodic theoryA closely related topic
- Go sideways: ErgodicityA closely related topic
📖 Definitions
Noun A system which is time-dependent.
🏆 Landmark papers (most cited)
Numerical integration of the cartesian equations of motion of a system with constraints: molecular dynamics of n-alkanes
Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions
Identification and control of dynamical systems using neural networks
Dynamical History of the Uranian System
Dynamical analysis, feedback control and synchronization of Liu dynamical system
Recurrence Time of a Dynamical System
The finite-dipole dynamical system
Sensitivity in Dynamical System Analysis†
🆕 Influential since 2022
Modern Koopman Theory for Dynamical Systems
GLC_FCS30D: the first global 30 m land-cover dynamics monitoring product with a fine classification system for the period from 1985 to 2022 generated using dense-time-series Landsat imagery and the continuous change-detection method
Learning stochastic dynamical system via flow map operator
Dynamical system analysis of Myrzakulov gravity
Interpretable predictions of chaotic dynamical systems using dynamical system deep learning
📚 Books worth reading
ChaosJames Gleick · 1987
Nonlinear dynamics and ChaosSteven H. Strogatz, Steven Strogatz · 1994
Thinking in systemsDonella H. Meadows, Diana Wright · 2008
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector FieldsJohn Guckenheimer, Philip Holmes · 1983
DynamicsBenson H. Tongue, Sheri D. Sheppard · 2004
Chaos and fractalsHeinz-Otto Peitgen, Hartmut Jürgens · 1992- 📕Dynamic SystemsCraig A. Kluever · 2015
World dynamicsJay Wright Forrester · 1971
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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