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Three-Dimensional State Space and Chaos

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/9780198507239.003.0004
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter extends state space descriptions to systems with three (or more) dimensions. For systems described by differential equations, higher state space dimensions allow for more complex ... More


Two‐Dimensional Discrete Dynamical Systems

David P. Feldman

in Chaos and Fractals: An Elementary Introduction

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199566433
eISBN:
9780191774966
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199566433.003.0027
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Dynamical systems can be iterated functions of one continuous variable. An example of such a system is the iterated logistic equation. This chapter focuses on two-dimensional discrete dynamical ... More


Chaotic Differential Equations and Strange Attractors

David P. Feldman

in Chaos and Fractals: An Elementary Introduction

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199566433
eISBN:
9780191774966
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199566433.003.0032
Subject:
Physics, Theoretical, Computational, and Statistical Physics

For two-dimensional differential equations, aperiodic behaviour is not possible in the sense that trajectories in phase space cannot cross, which limits the behaviours that can arise on a ... 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


Chaos and the Explanatory Significance of Equilibrium: Strange Attractors in Evolutionary Game Dynamics

Brian Skyrms

in Social Dynamics

Published in print:
2014
Published Online:
June 2014
ISBN:
9780199652822
eISBN:
9780191779367
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199652822.003.0006
Subject:
Philosophy, Philosophy of Science

The explanatory significance of equilibrium depends on the underlying dynamics. The dynamics may, indeed, never reach equilibrium but rather cycle or even describe a chaotic orbit. This point is ... More


Nonlinear Dynamics and Chaos

David D. Nolte

in Introduction to Modern Dynamics: Chaos, Networks, Space, and Time

Published in print:
2019
Published Online:
November 2019
ISBN:
9780198844624
eISBN:
9780191880216
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198844624.003.0004
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The geometric structure of state space is understood through phase portraits and stability analysis that classify the character of fixed points based on the properties of Lyapunov exponents. Limit ... More


Attractors and Locked-In Art: Art History as a Complex System

Francis Halsall

in Speculative Art Histories: Analysis at the Limits

Published in print:
2017
Published Online:
May 2018
ISBN:
9781474421041
eISBN:
9781474438605
Item type:
chapter
Publisher:
Edinburgh University Press
DOI:
10.3366/edinburgh/9781474421041.003.0004
Subject:
Philosophy, Aesthetics

My speculation in this paper is to consider, in short, what if art history is a system? In other words what does it means to think about art through the systems-thinking. To do so would mean ... More


Bubba Ho-tep and the Seriously Silly Cult Film

Jeffrey Andrew Weinstock

in Science Fiction Double Feature: The Science Fiction Film as Cult Text

Published in print:
2015
Published Online:
May 2016
ISBN:
9781781381830
eISBN:
9781781382363
Item type:
chapter
Publisher:
Discontinued
DOI:
10.5949/liverpool/9781781381830.003.0016
Subject:
Film, Television and Radio, Film

This chapter uses Don Coscarelli's the science fiction (sf)/horror mash-up Bubba Ho-tep (2002) to propose that sf, fantasy, and indeed cult films of all stripes are both literal and figurative ... 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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