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Title Bifurcations : sights, sounds, and mathematics / T. Matsumoto ... [and others].

Published Tokyo ; New York : Springer, 1993.


Location Call No. Status
 UniM Store Engin  003.85 BIFU    AVAILABLE
Physical description xiii, 468 pages : illustrations ; 24 cm
Bibliography Includes bibliographical references (pages 445-457) and index.
Contents 1. Bifurcations Observed from Electronic Circuits. 1.2. The Double Scroll Circuit. 1.3. Structure of the Double Scroll. 1.4. The Double Scroll Circuit is Chaotic in the Sense of Shil'nikov. 1.5. Homoclinic Linkage. 1.6. The Torus Breakdown Circuit. 1.7. The Hyperchaotic Circuit. 1.8. The Neon Bulb Circuit. 1.9. The R-L-Diode Circuit -- 2. Bifurcations of Continuous Piecewise-Linear Vector Fields. 2.2. Definition and Standard Forms of Continuous Piecewise-Linear Maps. 2.3. Normal Forms of Piecewise-Linear Vector Fields. 2.4. Multiregion Systems and Chaotic Attractors. 2.5. Bifurcation Equations of Piecewise-Linear Vector Fields. 2.6. Bifurcation Sets -- 3. Fundamental Concepts in Bifurcations. 3.2. Fundamental Notions for Dynamical Systems. 3.3. Local Bifurcations around Equilibrium Points in Vector Fields. 3.4. Dynamics and Bifurcations for Discrete Dynamical Systems. 3.5. Bifurcations of Homoclinic and Heteroclinic Orbits in Vector Fields.
Summary This book consists of three chapters. Chapter 1 presents concrete experimental results on bifurcations/chaos, performed on electronic circuits together with theoretical analysis. Chapter 2 presents a rigorous systematic treatment of bifurcations of piecewise-linear vector fields. Chapter 3 provides the reader with fundamental concepts, as well as ideas of bifurcations. Both Chapters 2 and 3 provide the theoretical background of the experiments presented in Chapter 1. Many color figures are also provided to facilitate the reader's understanding of the materials. Since the circuits in the book are simple, the amateur or novice reader can also build them, and observe and listen to the bifurcations/chaos, since the circuits are designed to behave within audible frequencies.
Other author Matsumoto, T. (Takashi), 1944-
Subject Electronic circuits -- Mathematical models.
Bifurcation theory.
Chaotic behavior in systems.
ISBN 0387701206 (New York : alk. paper)
4431701206 (Tokyo : alk. paper)
3540701206 (Berlin : alk. paper)