This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. 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, and strange attractors.
A unique feature of the book is its emphasis on applications. These include mechanical vibrations, lasers, biological rhythms, superconducting circuits, insect outbreaks, chemical oscillators, genetic control systems, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with mathematical theory.
In the twenty years since the first edition of this book appeared, the ideas and techniques of nonlinear dynamics and chaos have found application to such exciting fields as systems biology, evolutionary game theory, and socio-physics. This second edition includes new exercises on these cutting-edge developments, on topics as varied as curiosities of visual perception and the tumultuous love dynamics in Gone with the Wind.
"The new edition has a friendly yet clear technical style . . . One of the book's biggest strengths is that it explains core concepts through practical examples drawn from various fields and from real-world systems . . . the author's excellent use of geometric and graphical techniques greatly clarifies what can be amazingly complex behavior." Physics Today
"Nonlinear Dynamics and Chaos is an excellent book that effectively demonstrates the power and beauty of the theory of dynamical systems. Its readers will want to learn more." Mathematical Association of America
PART I. ONE-DIMENSIONAL FLOWS
2. Flows on the Line
4. Flows on the Circle
PART II. TWO-DIMENSIONAL FLOWS
5. Linear Systems
6. Phase Plane
7. Limit Cycles
8. Bifurcations Revisited
PART III. CHAOS
9. Lorenz Equations
10. One-Dimensional Maps
12. Strange Attractors
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