Student Solutions Manual for Nonlinear Dynamics and Chaos, Second Edition


Mitchal Dichter

Second Edition • July 12, 2016 • 404 pages


Print ISBN: 9780813350547 • $19.99 USD$25.99 CAN

Ebook ISBN: 9780813350554 • $9.99 USD$12.99 CAN

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This book is a companion to Nonlinear Dynamics and Chaos, second edition, by Steven H. Strogatz

This book is a companion to Nonlinear Dynamics and Chaos, second edition, by Steven H. Strogatz

This official Student Solutions Manual includes solutions to the odd-numbered exercises featured in the Second Edition of Steven Strogatz’s classic text Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. The textbook and accompanying Student Solutions Manual are aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. Complete with graphs and worked-out solutions, this manual demonstrates techniques for students to analyze differential equations, bifurcations, chaos, fractals, and other subjects Strogatz explores in his popular book.


Mitchal Dichter is an instructor of math at Campus Learning Assistance Services at the University of California, Santa Barbara.

CONTENTS
2: Flows on the Line
2.1 A Geometric Way of Thinking
2.2 Fixed Points and Stability
2.3 Population Growth
2.4 Linear Stability Analysis
2.5 Existence and Uniqueness
2.6 Impossibility of Oscillations
2.7 Potentials
2.8 Solving Equations on the Computer

3: Bifurcations
3.1 Saddle-Node Bifurcation
3.2 Transcritical Bifurcation
3.3 Laser Threshold
3.4 Pitchfork Bifurcation
3.5 Overdamped Bead on a Rotating Hoop
3.6 Imperfect Bifurcations and Catastrophes
3.7 Insect Outbreak

4: Flows on the Circle
4.1 Examples and Definitions
4.2 Uniform Oscillator
4.3 Nonuniform Oscillator
4.4 Overdamped Pendulum
4.5 Fireflies
4.6 Superconducting Josephson Junctions

5: Linear Systems
5.1 Definitions and Examples
5.2 Classification of Linear Systems
5.3 Love Affairs

6 Phase Plane
6.1 Phase Portraits
6.2 Existence, Uniqueness, and Topological Consequences
6.3 Fixed Points and Linearization
6.4 Rabbits versus Sheep
6.5 Conservative Systems
6.6 Reversible Systems
6.7 Pendulum
6.8 Index Theory

7: Limit Cycles
7.1 Examples
7.2 Ruling Out Closed Orbits
7.3 Poincar´e-Bendixson Theorem
7.4 Li´enard Systems
7.5 Relaxation Oscillations
7.6 Weakly Nonlinear Oscillators

8: Bifurcations Revisited
8.1 Saddle-Node, Transcritical, and Pitchfork Bifurcations
8.2 Hopf Bifurcations
8.3 Oscillating Chemical Reactions
8.4 Global Bifurcations of Cycles
8.5 Hysteresis in the Driven Pendulum and Josephson Junction
8.6 Coupled Oscillators and Quasiperiodicity
8.7 Poincar´e Maps

9: Lorenz Equations
9.1 A Chaotic Waterwheel
9.2 Simple Properties of the Lorenz Equations
9.3 Chaos on a Strange Attractor
9.4 Lorenz Map
9.5 Exploring Parameter Space
9.6 Using Chaos to Send Secret Messages

10: One-Dimensional Maps
10.1 Fixed Points and Cobwebs
10.2 Logistic Map: Numerics
10.3 Logistic Map: Analysis
10.4 Periodic Windows
10.5 Liapunov Exponent
10.6 Universality and Experiments
10.7 Renormalization

11: Fractals
11.1 Countable and Uncountable Sets
11.2 Cantor Set
11.3 Dimension of Self-Similar Fractals
11.4 Box Dimension
11.5 Pointwise and Correlation Dimensions

12: Strange Attractors
12.1 The Simplest Examples
12.2 H´enon Map
12.3 R¨ossler System
12.4 Chemical Chaos and Attractor Reconstruction
12.5 Forced Double-Well Oscillator

Praise for Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, Second Edition

“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

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