Exploring Chaos: Theory And Experiment
This book presents elements of the theory of chaos in dynamical systems in a framework of theoretical understanding coupled with numerical and graphical experimentation. The theory is developed using only elementary calculus and algebra, and includes dynamics of one-and two-dimensional maps, periodic orbits, stability and its quantification, chaotic behavior, and bifurcation theory of one-dimensional systems. There is an introduction to the theory of fractals, with an emphasis on the importance…
Read More ↓Title Statements
- Full title :Exploring Chaos : Theory And Experiment / Brian Davies.
Summary
This book presents elements of the theory of chaos in dynamical systems in a framework of theoretical understanding coupled with numerical and graphical experimentation. The theory is developed using only elementary calculus and algebra, and includes dynamics of one-and two-dimensional maps, periodic orbits, stability and its quantification, chaotic behavior, and bifurcation theory of one-dimensional systems. There is an introduction to the theory of fractals, with an emphasis on the importance of scaling, and a concluding chapter on ordinary differential equations. The accompanying software, written in Java, is available online (see link below) The program enables students to carry out their own quantitative experiments on a variety of nonlinear systems, including the analysis of fixed points of compositions of maps, calculation of Fourier spectra and Lyapunov exponents, and box counting for two-dimensional maps. It also provides for visualizing orbits, final state and bifurcation diagrams, Fourier spectra and Lyapunov exponents, basins of attractions, three-dimensional orbits, Poincar?ections, and return maps. Please visit http://www.maths.anu.edu.au/b̃riand/chaos/ for the integrated cross-platform software.
Read More ↓Edition Statements
- Publication Date:2018.
Publication Statements
- Publisher(s):CRC Press
- Place of Publication:Boca Raton, FL
- Language:eng
- Publication Date:2018.
The Physical Object
- Description:1 online resource
Edition Identifiers
- ISBN:9780786745616, 0786745614, 9780429971419, 0429971419
- oclc:on1035845157
- LC Classification:QA614.8
- Dewey Decimal:003/.857
Table of Contents
Cover; Half Title; Title Page; Copyright Page; Dedication; Preface; Table of Contents; 1: Introduction; 1.1 Dynamical models; 1.2 Celestial mechanics; 1.3 Lorenz: the end of weather prediction?; 1.4 Complex behaviour of simple systems; 2: Orbits of one-dimensional systems; 2.1 Discrete dynamical systems; 2.2 Fixed points and stability; 2.3 Some orbits of the tent map; 2.4 Period doubling of the logistic map; 2.5 Periodic orbits and compositions; 2.6 The fully chaotic tent map; 2.7 Numerical versus exact orbits; 2.8 Fourier analysis of an orbit; 2.9 Lyapunov exponent of an orbit
2.10 Chaotic orbits2.11 Ergodic orbits; 3: Bifurcations in one-dimensional systems; 3.1 Bifurcation diagrams; 3.2 Final state diagrams; 3.3 Period doubling mechanism; 3.4 Period doubling cascades; 3.5 Feigenbaum's universal constants; 3.6 Tangent bifurcations; 3.7 Intermittent behaviour; 3.8 Unstable orbits and crises; 3.9 Transcritical and pitchfork bifurcations; 3.10 Theory of Feigenbaum scaling; 4: Two-dimensional systems; 4.1 The Hénon map; 4.2 Fixed points; 4.3 Area contraction; 4.4 Stability of fixed points; 4.5 Periodic orbits; 4.6 Lyapunov exponents; 4.7 Basin boundaries
4.8 Linear feedback and co…
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