,Student Solutions Manual for
Nonlinear Dynamics and Chaos,
Third Edition
With Applications to Physics, Biology,
Chemistry and Engineering
Mitchal Dichter
Boca Raton London New York
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© 2024 Mitchal Dichter
First edition published by Westview Press 2017
Second edition published by Taylor and Francis 2018
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ISBN 13: 978-0-367-26566-3 (pbk)
ISBN 13: 978-0-429-29397-9 (ebk)
DOI: 10.1201/9780429293979
, CONTENTS
Part I One-Dimensional Flows
2 Flows on the Line 1
2.1 A Geometric Way of Thinking 1
2.2 Fixed Points and Stability 2
2.3 Population Growth 6
2.4 Linear Stability Analysis 8
2.5 Existence and Uniqueness 10
2.6 Impossibility of Oscillations 11
2.7 Potentials 12
2.8 Solving Equations on the Computer 13
3 Bifurcations 17
3.1 Saddle-Node Bifurcation 17
3.2 Transcritical Bifurcation 25
3.3 Laser Threshold 28
3.4 Pitchfork Bifurcation 30
3.5 Overdamped Bead on a Rotating Hoop 40
3.6 Imperfect Bifurcations and Catastrophes 42
3.7 Insect Outbreak 51
4 Flows on the Circle 61
4.1 Examples and Definitions 61
4.2 Uniform Oscillator 62
4.3 Nonuniform Oscillator 62
4.4 Overdamped Pendulum 70
4.5 Fireflies 73
4.6 Superconducting Josephson Junctions 75
Part II Two-Dimensional Flows
5 Linear Systems 81
5.1 Definitions and Examples 81
5.2 Classification of Linear Systems 86
5.3 Love Affairs 94
6 Phase Plane 96
6.1 Phase Portraits 96
6.2 Existence, Uniqueness, and Topological Consequences 102
6.3 Fixed Points and Linearization 103
6.4 Rabbits versus Sheep 111
6.5 Conservative Systems 123
6.6 Reversible Systems 137
6.7 Pendulum 152
6.8 Index Theory 154
