Unlike most other texts, which emphasize either classical methods, experiments and physics, geometrical methods, computational methods, or applied mathematics, Applied Nonlinear Dynamics blends these approaches to provide a unified treatment of nonlinear dynamics. Further, it presents mathematical concepts in a manner comprehensible to engineers and applied scientists. The synthesis of analytical, experimental, and numerical methods and the inclusion of many exercises and worked-out examples will make this the textbook of choice for classroom teaching. Moreover, the inclusion of an extensive and up-to-date bibliography will make it an invaluable text for professional reference.

### CONTENTS

• PREFACE
• Chapter 1: INTRODUCTION
• 1.1 Discrete-Time Systems
• 1.2 Continuous-Time Systems
• 1.3 Attracting Sets
• 1.4 Concepts of Stability
• 1.5 Attractors
• 1.7 Exercises
• Chapter 2: EQUILIBRIUM SOLUTIONS
• 2.1 Continuous-Time Systems
• 2.2 Fixed Points of Maps
• 2.3 Bifurcations of Continuous Systems
• 2.4 Bifurcations of Maps
• 2.5 Exercises
• Chapter 3: PERIODIC SOLUTIONS
• 3.1 Periodic Solutions
• 3.2 Floquet Theory
• 3.3 Poincare Maps
• 3.4 Bifurcations
• 3.5 Analytical Constructions
• 3.6 Exercises
• Chapter 4: QUASIPERIODIC SOLUTIONS
• 4.1 Poincare Maps
• 4.2 Circle Map
• 4.3 Constructions
• 4.4 Stability
• 4.5 Synchronization
• 4.6 Exercises
• Chapter 5: CHAOTIC SOLUTIONS
• 5.1 Maps
• 5.2 Continuous-Time Systems
• 5.3 Period-Doubling Scenario
• 5.4 Intermittency Mechanisms
• 5.5 Quasiperiodic Routes
• 5.6 Crises
• 5.7 Melnikov Theory
• 5.8 Bifurcations of Homoclinic Orbits
• 5.9 Exercises
• Chapter 6: NUMERICAL METHODS
• 6.1 Continuation of Fixed Points
• 6.2 Simple Turning and Branch Points
• 6.3 Hopf Bifurcation Points
• 6.4 Homotopy Algorithms
• 6.5 Construction of Periodic Solutions
• 6.6 Continuation of Periodic Solutions
• Chapter 7: TOOLS TO ANALYZE MOTIONS
• 7.1 Introduction
• 7.2 Time Histories
• 7.3 State Space
• 7.4 Pseudo-State Space
• 7.5 Fourier Spectra
• 7.6 Poincare Sections and Maps
• 7.7 Autocorrelation Functions
• 7.8 Lyapunov Exponents
• 7.9 Dimension Calculations
• 7.10 Higher-Order Spectra
• 7.11 Exercises
• Chapter 8: CONTROL
• 8.1 Control of Bifurcations
• 8.2 Chaos Control
• 8.3 Synchronization
• BIBLIOGRAPHY
• SUBJECT INDEX

Book ISBN: 0-471-59348-6
Wiley-Interscience
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### BOOK REVIEWS

• Applied Mechanics Reviews, Vol. 48(7), July 1995
• SIAM Review, Vol. 38(2), June 1996
• Pure Appl. Geophysics, Vol. 150, 1997