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Iterated Maps

Robert C. Hilborn

in Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers

Published in print:
2000
Published Online:
January 2010
ISBN:
9780198507239
eISBN:
9780191709340
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507239.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Dynamical systems described by iterated map functions are used to explore the period-doubling route to chaos, Lyapunov exponents, and Feigenbaum numbers. A simple derivation of the numerical value of ... More


Some Simulation Tools for Tracking Continuous Mental Trajectories

Michael Spivey

in The Continuity of Mind

Published in print:
2006
Published Online:
September 2007
ISBN:
9780195170788
eISBN:
9780199786831
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195170788.003.0004
Subject:
Psychology, Cognitive Neuroscience

This chapter promotes quantitative simulation as an important accompaniment to theoretical and experimental methods in dynamical approaches to understanding the mind. A mathematical introduction is ... More


Three Chaotic Systems

Robert C. Hilborn

in Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers

Published in print:
2000
Published Online:
January 2010
ISBN:
9780198507239
eISBN:
9780191709340
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507239.003.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter introduces chaotic behaviour by examining three systems — an electronic circuit, an iterated map model (the logistic map), and a set of differential equations (the Lorenz model) — and ... More


Linear and Nonlinear Dynamic Behaviour

Ray Huffaker, Marco Bittelli, and Rodolfo Rosa

in Nonlinear Time Series Analysis with R

Published in print:
2017
Published Online:
February 2018
ISBN:
9780198782933
eISBN:
9780191826153
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198782933.003.0002
Subject:
Physics, Theoretical, Computational, and Statistical Physics

In this chapter, we describe how highly erratic dynamic behavior can arise from a nonlinear logistic map, and how this apparently random behavior is governed by a surprising order. With this lesson ... More


Nonlinear systems∗

Chun Wa Wong

in Introduction to Mathematical Physics: Methods & Concepts

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199641390
eISBN:
9780191747786
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199641390.003.0006
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Nonlinear systems show two very different faces: unpredictability and unusual coherence. Unpredictability is shown to arise from instabilities and bifurcations that are highly sensitive to small ... More


From Butterflies to Hurricanes

David D. Nolte

in Galileo Unbound: A Path Across Life, the Universe and Everything

Published in print:
2018
Published Online:
August 2018
ISBN:
9780198805847
eISBN:
9780191843808
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198805847.003.0009
Subject:
Physics, History of Physics

Half a century after Poincaré first glimpsed chaos in the three-body problem, the great Russian mathematician Andrey Kolmogorov presented a sketch of a theorem that could prove that orbits are ... More


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