Gourt > Science > Math > Differential Equations > Dynamical Systems (6)
A dynamical system is a concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space. The mathematical models used to describe the swinging of a clock pendulum, the flow of water in a pipe, or the number of fish each spring in a lake are examples of dynamical systems.
A dynamical system has a state determined by a collection of real numbers. Small changes in the state of the system correspond to small changes in the numbers. The numbers are also the coordinates of a geometrical space—a manifold. The evolution rule of the dynamical system is a fixed rule that describes what future states follow from the current state. The rule is deterministic: for a given time interval only one future state follows from the current state.
Overview
The concept of dynamical system has its origins in Newtonian mechanics. There, as in other natural sciences and engineering disciplines, the evolution rule of dynamical systems is given implicitly by a relation that gives the state of the system only a short time into the future. (The relation is either a differential equation or difference equation.) To determine the state for all future times requires iterating the relation many times—each advancing time a small step. The iteration procedure is referred to as solving the system or integrating the system. Once the system can be solved, given an initial point it is possible to determine all its future points, a collection known as a trajectory or orbit. More on [ Dynamical system ]
Difference Equations :: Differential Equations
Business Math For Dummies
Mary Jane Sterling Mon, 30 Jun 2008 04:00:00 -0000
The essential desk reference for every business professional or student This easy-to-understand resource explains complex mathematical concepts and formulas and offers clear examples of how they relate to real-world business situations. Featuring practical practice problems to help readers hone their skills, it covers such key topics as working with percents to calculate increases and decreases, Read More...
Uncertainty in Industrial Practice: A Guide to Quantitative Uncertainty Management
Etienne de Rocquigny (Editor), Dr. Nicolas Devictor (Editor), Dr. Stefano Tarantola (Editor) Mon, 30 Jun 2008 04:00:00 -0000
There is a growing demand from institutional bodies for the justification of industrial methodologies and practices (e.g. safety criteria, environmental protection and control, maintenance and design optimization). Previous books in this area have either been too theoretical, or too specific in their scope. Uncertainty in Industrial Practice aims to provide a practical reference on uncertainty treatment for all types of industry, Read More...
Generalized, Linear, and Mixed Models, 2nd Edition
Charles E. McCulloch, Shayle R. Searle, John M. Neuhaus Mon, 30 Jun 2008 04:00:00 -0000
An accessible and self-contained introduction to statistical models-now in a modernized new edition Generalized, Linear, and Mixed Models, Second Edition provides an up-to-date treatment of the essential techniques for developing and applying a wide variety of statistical models. The book presents thorough and unified coverage of the theory behind generalized, linear, and mixed models and highlights their similarities and differences in various Read More...
Bayesian Approach to Inverse Problems
Jérôme Idier (Editor) Mon, 30 Jun 2008 04:00:00 -0000
Many scientific, medical or engineering problems raise the issue of recovering some physical quantities from indirect measurements; for instance, detecting or quantifying flaws or cracks within a material from acoustic or electromagnetic measurements at its surface is an essential problem of non-destructive evaluation. The concept of inverse problems precisely originates from the idea of inverting the laws of physics to recover a quantity of interest Read More...
Time Series Analysis: Forecasting and Control, 4th Edition
George E. P. Box, Gwilym M. Jenkins, Gregory C. Reinsel Mon, 30 Jun 2008 04:00:00 -0000
This is a revision of a classic, seminal, and authoritative book that has been the model for most books on the topic written since 1970. It focuses on practical techniques throughout, rather than a rigorous mathematical treatment of the subject. It explores the building of stochastic (statistical) models for time series and their use in important areas of application forecasting, model specification, Read More...
Numerical Methods for Ordinary Differential Equations, 2nd Edition
John Butcher Mon, 23 Jun 2008 04:00:00 -0000
Authored by one of the world’s leading authorities on numerical methods this update of one of the standard references on numerical analysis, outlines recent developments in the field and presenting a detailed overview of the area. The only book to provide both a detailed treatment of Runge-Kutta methods and a thorough exposition of general linear methods, it also provides practical guidance on solving equations associated with general linear Read More...
ArXiv - Recent papers in dynamical systems at the ArXiv preprint server.
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Chaos, Limit Cycles and Twisted Rods - Integrability and chaotic attractors. Limit cycles of the Lienard systems. Elastic instabilites : twisted rods. Path and surface following : continuation algorithms.
Meta Description: [ Dr. Sebastien Neukirch : Research Fellow in dynamical systems ]
Climate Dynamics, Chaos and Quantum Mechanics - A general systems theory for chaos, quantum mechanics and climate dynamics applicable to dynamical systems of all space-time scales.
Crowd Dynamics - Crowd and Egress Dynamics by G. Keith Still.
Meta Description: [ Crowd Dynamics Limited are the international experts on how crowd form and move in places of public assembly during normal and emergency situations. ]
Dynamical Systems Data Base - Data base of around 50,000 planar dynamical systems.
Dynamical Systems Home Page - Conference listings, survey articles, open problems, people, jobs, and seminars.
Dynamical Systems Lab - This set of lectures is designed to explore one-dimensional dynamical systems using the software Chaos and Dynamics.
Dynamical Systems Websites - A list of research sites maintained at the University of Warwick.
Dynamics in One Complex Variable - These notes study the dynamics of iterated holomorphic mappings from a Riemann surface to itself. The reader is assumed to be familiar with the rudiments of complex variable theory and of two-dimensional differential geometry.
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Ergodic Theory and Dynamical Systems - With a particular emphasis on applications to other areas of mathematics. Mark Pollicott.
Meta Description: [ School of Mathematics, The University of Manchester ]
Evolution Equations and Semigroups - Bulletin board and preprint archive.
Java Exploration Tool for Dynamical Systems - This Java Applet can be used for the exploration on two-dimensional analytical defined dynamical systems. The system is defined by a set of two differential equations, which will be evaluated within adjustable regions forming a two-dimensional vector field.
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Nonlinear Dynamics Bibliography - Maintained by Peter E. Beckmann, Johannes Gutenberg Universität.
Meta Description: [ Nonlinear Dynamics Bibliography CHAOSBIB, BibTeX and REFs-Format ]
Pages on Dynamical Systems - A interactive laboratory on dynamical systems, in particular on particle systems.
Meta Description: [ Mathematical software and dynamical systems ]
Society for Nonlinear Dynamics and Econometrics - The Society seeks to promote the use of nonlinear methods in economics and finance from both a theoretical and empirical perspective.
Surveys in Dynamical Systems - References to several surveys and papers of introductory character which are available on-line.
Turbulent Landscapes - Turbulent Landscapes is the result of 13 artists' explorations of complexity in nature. The exhibit will travel to museums and science centers in upcoming months.
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