Dutton, John A. College of Earth and Mineral Sciences, Pennsylvania State University, University Park, Pennsylvania.
Lorenz, Edward N. Formerly, Center for Meteorology and Physical Oceanography, Massachusetts Institute of Technology, Cambridge, Massachusetts.
Peters, Randall D. Department of Physics, Mercer University, Macon, Georgia.
Jefferies, David J. Department of Electronic and Electrical Engineering, University of Surrey, Surrey, United Kingdom.
Murray, Carl D. Astronomy Unit, Queen Mary, University of London, London, United Kingdom.
Lauterborn, Werner Institut für Angewandte Physik, Technische Hochschule Darmstadt, Darmstadt, Germany.
Koch, Peter M. Department of Physics, State University of New York, Stony Brook, New York.
Last reviewed:November 2020
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- Highly ordered motion
- Ordered motion
- Chaotic motion
- Systems in the real world
- Chaos and periodicity
- Lorenz butterfly
- Lorenz model and equations
- Chaotic attractor
- Stretching, tearing, and folding
- Butterflies and computers
- Some mathematical foundations in physics
- Hamilton's equations and maps
- Iteration and numerical integration subtlety
- Examples in two dimensions
- Examples in one dimension
- Feigenbaum constant
- Atmospheric prediction
- Electronic circuits
- Static external fields
- Time-varying external fields
- Related Primary Literature
- Additional Reading
System behavior that depends so sensitively on the system's precise initial conditions that it is, in effect, unpredictable and cannot be distinguished from a random process, even though it is deterministic in a mathematical sense. This article begins with a discussion of the notions of order, chaos, and noise as they occur in deterministic dynamical systems, the relation of chaos and periodicity, and the concept of an attractor. Applications of chaos to atmospheric prediction, weather (Fig. 1), climate, electronic circuits, astronomy, acoustics, and atoms are then discussed.
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