Nonlinear Science FAQ

This FAQ about Nonlinear Science was compiled and written by James D. Meiss jdm@boulder.colorado.edu with numerous contributions by others.

(c) 1995-2003 by James D. Meiss, all rights reserved. This FAQ may be posted to any USENET newsgroup, on-line service, or BBS as long as it is posted in its entirety and includes this copyright statement. This FAQ may not be distributed for financial gain. This FAQ may not be included in commercial collections or compilations without express permission from the author.

2.1] What is nonlinear?
In geometry, linearity refers to Euclidean objects: lines, planes, (flat) ...
2.2] What is nonlinear science?
Stanislaw Ulam reportedly said (something like) Calling a science 'nonlinear' ...
2.3] What is a dynamical system? (nonlinear science)
A dynamical system consists of an abstract phase space or state space, whose ...
2.4] What is phase space? (nonlinear science)
Phase space is the collection of possible states of a dynamical system. A ...
2.5] What is a degree of freedom? (nonlinear science)
The notion of degrees of freedom as it is used for ...
2.6] What is a map? (nonlinear science)
A map is simply a function, f, on the phase space that gives the next state, ...
2.7] How are maps related to flows (differential equations)?
Every differential equation gives rise to a map, the time one map, defined by ...
2.8] What is an attractor? (nonlinear science)
Informally an attractor is simply a state into which a system settles (thus ...
2.9] What is chaos? (nonlinear science)
It has been said that Chaos is a name for any order that produces confusion ...
2.10] What is sensitive dependence on initial conditions? (nonlinear science)
Consider a boulder precariously perched on the top of an ideal hill. The ...
2.11] What are Lyapunov exponents? (nonlinear science)
(Thanks to Ronnie Mainieri & Fred Klingener for contributing to this answer)...
2.12] What is a Strange Attractor? (nonlinear science)
Before Chaos (BC?), the only known attractors (see [2.8]) were fixed ...
2.13] Can computers simulate chaos? (nonlinear science)
Strictly speaking, chaos cannot occur on computers because they deal with ...
2.14] What is generic? (nonlinear science)
(Thanks to Hawley Rising for contributing to this answer)...
2.15] What is the minimum phase space dimension for chaos? (nonlinear science)
This is a slightly confusing topic, since the answer depends on the type of ...
3.1] What are complex systems? (nonlinear science)
(Thanks to Troy Shinbrot for contributing to this answer)...
3.2] What are fractals? (nonlinear science)
One way to define fractal is as a negation: a fractal is a set that does not ...
3.3] What do fractals have to do with chaos?
Often chaotic dynamical systems exhibit fractal structures in phase space. ...
3.4] What are topological and fractal dimension?
See the fractal FAQ:...
3.5] What is a Cantor set? (nonlinear science)
(Thanks to Pavel Pokorny for contributing to this answer)...
3.6] What is quantum chaos? (nonlinear science)
(Thanks to Leon Poon for contributing to this answer)...
3.7] How do I know if my data are deterministic? (nonlinear science)
(Thanks to Justin Lipton for contributing to this answer)...
3.8] What is the control of chaos? (nonlinear science)
Control of chaos has come to mean the two things:...
3.9] How can I build a chaotic circuit? (nonlinear science)
(Thanks to Justin Lipton and Jose Korneluk for contributing to this answer)...
3.10] What are simple experiments to demonstrate chaos? (nonlinear science)
There are many chaos toys on the market. Most consist of some sort of ...
3.11] What is targeting? (nonlinear science)
(Thanks to Serdar Iplikçi for contributing to this answer)...
3.12] What is time series analysis? (nonlinear science)
(Thanks to Jim Crutchfield for contributing to this answer)...
3.13] Is there chaos in the stock market? (nonlinear science)
(Thanks to Bruce Stewart for Contributions to this answer)...
3.14] What are solitons? (nonlinear science)
The process of obtaining a solution of a linear (constant coefficient) ...
3.15] What is spatio-temporal chaos? (nonlinear science)
Spatio-temporal chaos occurs when system of coupled dynamical systems ...
3.16] What are cellular automata? (nonlinear science)
(Thanks to Pavel Pokorny for Contributions to this answer)...
3.17] What is a Bifurcation? (nonlinear science)
(Thanks to Zhen Mei for Contributions to this answer)...
3.18] What is a Hamiltonian Chaos? (nonlinear science)
The transition to chaos for a Hamiltonian (conservative) system is somewhat ...
4.2] What technical journals have nonlinear science articles?
Physica D The premier journal in Applied Nonlinear ...
4.3] What are net sites for nonlinear science materials?
5.1] What are general computational resources? (nonlinear science)
CAIN Europe ...
5.2.1] Where can I find specialized programs for nonlinear science? A-D
5.2.2] Where can I find specialized programs for nonlinear science? F-L
5.2.3] Where can I find specialized programs for nonlinear science? M-S
Macintosh Dynamics ...
5.2.4] Where can I find specialized programs for nonlinear science? T-X
Time Series ...
6] Acknowledgments (sci.nonlinear)
Alan Champneys a.r.champneys@bristol.ac....