Nonlinear Dynamics and Chaos, Third Edition
Chapman & Hall/CRC (Verlag)
978-1-032-66521-4 (ISBN)
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The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, strange attractors, and synchronization.
The prerequisites are comfort with multivariable calculus and linear algebra, as well as a first course in physics.
Changes to this edition include substantial exercises about conceptual models of climate change, an updated treatment of the SIR model of epidemics, and amendments (based on recent research) about the Selkov model of oscillatory glycolysis. Equations, diagrams, and explanations have been reconsidered and often revised. There are also about 50 new references, many from the recent literature.
The most notable change is a new chapter about the Kuramoto model.
This icon of nonlinear dynamics, introduced in 1975 by the Japanese physicist Yoshiki Kuramoto, is one of the rare examples of a high-dimensional nonlinear system that can be solved by elementary means. It provides an entrée to current research on complex systems, synchronization, and networks, yet is accessible to newcomers.
Students and teachers have embraced the book in the past for its exceptional clarity and rich applications, and its general approach and framework continue to be sound.
Steven Strogatz is the Schurman Professor of Applied Mathematics at Cornell University. His honors include MIT's highest teaching prize, a lifetime achievement award for the communication of mathematics to the general public, and membership in the American Academy of Arts and Sciences. His research on a wide variety of nonlinear systems from synchronized fireflies to small-world networks has been featured in the pages of Scientific American, Nature, Discover, Business Week, and The New York Times.
Chapter 1. Overview. Chapter 2. Flows on the Line. Chapter 3. Bifurcations. Chapter 4. Flows on the Circle. Chapter 5. Linear Systems. Chapter 6. Phase Plane. Chapter 7. Limit Cycles. Chapter 8. Bifurcations Revisited. Chapter 9. Lorenz Equations. Chapter 10. One-Dimensional Maps. Chapter 11. Fractals. Chapter 12. Strange Attractors. Chapter 13. Kuramoto Model.
| Erscheint lt. Verlag | 9.2.2024 |
|---|---|
| Zusatzinfo | 351 Halftones, black and white; 351 Illustrations, black and white |
| Sprache | englisch |
| Maße | 156 x 234 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Naturwissenschaften ► Physik / Astronomie | |
| ISBN-10 | 1-032-66521-1 / 1032665211 |
| ISBN-13 | 978-1-032-66521-4 / 9781032665214 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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