Elegant chaos algebraically simple chaotic flows.
This heavily illustrated book collects in one source most of the mathematically simple systems of differential equations whose solutions are chaotic. It includes the historically important systems of van der Pol, Duffing, Ueda, Lorenz, Rössler, and many others, but it goes on to show that there are...
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| Language: | English |
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New Jersey
World Scientific Publishing Co. Pte. Ltd
2010
World Scientific World Scientific Publishing Company WORLD SCIENTIFIC WSPC |
| Subjects: | |
| ISBN: | 9812838813, 9789812838810, 9789812838827, 9812838821, 9813203544, 9789813203549 |
| Online Access: | Get full text |
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| Abstract | This heavily illustrated book collects in one source most of the mathematically simple systems of differential equations whose solutions are chaotic. It includes the historically important systems of van der Pol, Duffing, Ueda, Lorenz, Rössler, and many others, but it goes on to show that there are many other systems that are simpler and more elegant. Many of these systems have been only recently discovered and are not widely known. Most cases include plots of the attractor and calculations of the spectra of Lyapunov exponents. Some important cases include graphs showing the route to chaos. The book includes many cases not previously published as well as examples of simple electronic circuits that exhibit chaos. |
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| AbstractList | This heavily illustrated book collects in one source most of the mathematically simple systems of differential equations whose solutions are chaotic. It includes the historically important systems of van der Pol, Duffing, Ueda, Lorenz, Rössler, and many others, but it goes on to show that there are many other systems that are simpler and more elegant. Many of these systems have been only recently discovered and are not widely known. Most cases include plots of the attractor and calculations of the spectra of Lyapunov exponents. Some important cases include graphs showing the route to chaos. The book includes many cases not previously published as well as examples of simple electronic circuits that exhibit chaos.No existing book thus far focuses on mathematically elegant chaotic systems. This book should therefore be of interest to chaos researchers looking for simple systems to use in their studies, to instructors who want examples to teach and motivate students, and to students doing independent study.Sample Chapter(s)Chapter 1: Fundamentals (2,231 KB)Contents: FundamentalsPeriodically Forced SystemsAutonomous Dissipative SystemsAutonomous Conservative SystemsLow-Dimensional Systems (D < 3)High-Dimensional Systems (D > 3)Circular SystemsSpatiotemporal SystemsTime-Delay SystemsChaotic Electrical CircuitsReadership: Chaos researchers, instructors and students interested in seeing elegant examples of chaotic systems. This heavily illustrated book collects in one source most of the mathematically simple systems of differential equations whose solutions are chaotic. It includes the historically important systems of van der Pol, Duffing, Ueda, Lorenz, Rössler, and many others, but it goes on to show that there are many other systems that are simpler and more elegant. Many of these systems have been only recently discovered and are not widely known. Most cases include plots of the attractor and calculations of the spectra of Lyapunov exponents. Some important cases include graphs showing the route to chaos. The book includes many cases not previously published as well as examples of simple electronic circuits that exhibit chaos. No existing book thus far focuses on mathematically elegant chaotic systems. This book should therefore be of interest to chaos researchers looking for simple systems to use in their studies, to instructors who want examples to teach and motivate students, and to students doing independent study. This heavily illustrated book collects in one source most of the mathematically simple systems of differential equations whose solutions are chaotic. It includes the historically important systems of van der Pol, Duffing, Ueda, Lorenz, Rössler, and many others, but it goes on to show that there are many other systems that are simpler and more elegant. Many of these systems have been only recently discovered and are not widely known. Most cases include plots of the attractor and calculations of the spectra of Lyapunov exponents. Some important cases include graphs showing the route to chaos. The book includes many cases not previously published as well as examples of simple electronic circuits that exhibit chaos. |
| Author | Sprott, Julien Clinton |
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| Keywords | Chaos Dynamical Systems Electronic Circuits Strange Attractors Differential Equations Fractals Oscillators Mathematical Models |
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| Notes | Includes bibliography (p. 265-280) and index |
| PageCount | 302 |
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| Publisher | World Scientific Publishing Co. Pte. Ltd World Scientific World Scientific Publishing Company WORLD SCIENTIFIC WSPC |
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| Snippet | This heavily illustrated book collects in one source most of the mathematically simple systems of differential equations whose solutions are chaotic. It... |
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| SubjectTerms | All Nonlinear Science Titles Chaotic behavior in systems Chaotic behavior in systems -- Mathematics Differential equations, Nonlinear Electrical & Electronic Engineering (Circuits & Systems, Communications, Control, Computer Engineering) Flows (Differentiable dynamical systems) Lyapunov exponents Mathematical Physics SCIENCE Statistical Physics, Complexity and Nonlinear Dynamical Systems |
| SubjectTermsDisplay | Chaotic behavior in systems Flows (Differentiable dynamical systems) Lyapunov exponents |
| Subtitle | algebraically simple chaotic flows. |
| TableOfContents | Elegant chaos : algebraically simple chaotic flows -- Preface -- Contents -- List of Tables -- Chapter 1: Fundamentals -- Chapter 2: Periodically Forced Systems -- Chapter 3: Autonomous Dissipative Systems -- Chapter 4: Autonomous Conservative Systems -- Chapter 5: Low-dimensional Systems (D<3) -- Chapter 6: High-dimensional Systems (D>3) -- Chapter 7: Circulant Systems -- Chapter 8: Spatiotemporal Systems -- Chapter 9: Time-Delay Systems -- Chapter 10: Chaotic Electrical Circuits -- Bibliography -- Index |
| Title | Elegant chaos |
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