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Chaos and Nonlinear DynamicsAn Introduction for Scientists and Engineers$
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Robert C. Hilborn

Print publication date: 2000

Print ISBN-13: 9780198507239

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780198507239.001.0001

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Pattern Formation and Spatiotemporal Chaos

Pattern Formation and Spatiotemporal Chaos

(p.433) 11 Pattern Formation and Spatiotemporal Chaos
Chaos and Nonlinear Dynamics

Robert C. Hilborn

Oxford University Press

When a dynamical system has significant spatial extent, its nonlinear dynamics can lead to the spontaneous formation of spatial patterns. Such systems provide models for how nature might have developed ordered, spatial structures from disordered states. Examples are given from fluid flow, transport models, coupled-oscillator modes, cellular automata, transport models, and reaction-diffusion systems. Diffusion-limited aggregation, viscous fingering, and dielectric breakdown provide further examples of pattern formation. Fractal structures make another appearance in this new context. This chapter also explores the somewhat controversial topic of self-organized criticality which has been put forward as an explanation for the occurrence of fractal structures in nature.

Keywords:   pattern formation, fluid flow, coupled oscillators, cellular automata, reaction-diffusion models, fractal dimension, self-organized criticality

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