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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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