On this webpage you will find my solutions to the second edition of "Nonlinear Dynamics and Chaos with Applications to Physics, Biology, Chemistry, and Engineering" by Steven H. Strogatz. Here is a link to the book's page on amazon.com. If you find my work useful, please consider making a donation. Thank you.
- Chapter 2: Flows on the Line
- Section 2.1: A Geometric Way of Thinking
- Section 2.2: Fixed Points and Stability
- Section 2.3: Population Growth
- Section 2.4: Linear Stability Analysis
- Section 2.5: Existence and Uniqueness
- Section 2.6: Impossibility of Oscillations
- Section 2.7: Potentials
- Section 2.8: Solving Equations on the Computer
- Chapter 3: Bifurcations
- Section 3.1: Saddle-Node Bifurcation
- Section 3.2: Transcritical Bifurcation
- Section 3.3: Laser Threshold
- Section 3.4: Pitchfork Bifurcation
- Section 3.5: Overdamped Bead on a Rotating Hoop
- Section 3.6: Imperfect Bifurcations and Catastrophes
- Section 3.7: Insect Outbreak
- Chapter 4: Flows on the Circle
- Section 4.1: Examples and Definitions
- Section 4.2: Uniform Oscillator
- Section 4.3: Nonuniform Oscillator
- Section 4.4: Overdamped Pendulum
- Section 4.5: Fireflies
- Section 4.6: Superconducting Josephson Junctions
- Chapter 5: Linear Systems
- Section 5.1: Definitions and Examples
- Section 5.2: Classification of Linear Systems
- Section 5.3: Love Affairs
- Chapter 6: Phase Plane
- Section 6.1: Phase Portraits
- Section 6.2: Existence, Uniqueness, and Topological Consequences
- Section 6.3: Fixed Points and Linearization
- Section 6.4: Rabbits versus Sheep
- Section 6.5: Conservative Systems
- Section 6.6: Reversible Systems
- Section 6.7: Pendulum
- Section 6.8: Index Theory
- Chapter 7: Limit Cycles
- Section 7.1: Examples
- Section 7.2: Ruling Out Closed Orbits
- Section 7.3: Poincaré-Bendixson Theorem
- Section 7.4: Liénard Systems
- Section 7.5: Relaxation Oscillations
- Section 7.6: Weakly Nonlinear Oscillators
- Chapter 8: Bifurcations Revisited
- Section 8.1: Saddle-Node, Transcritical, and Pitchfork Bifurcations
- Section 8.2: Hopf Bifurcations
- Section 8.3: Oscillating Chemical Reactions
- Section 8.4: Global Bifurcations of Cycles
- Section 8.5: Hysteresis in the Driven Pendulum and Josephson Junction
- Section 8.6: Coupled Oscillators and Quasiperiodicity
- Section 8.7: Poincaré Maps
- Chapter 9: Lorenz Equations
- Section 9.1: A Chaotic Waterwheel
- Section 9.2: Simple Properties of the Lorenz Equations
- Section 9.3: Chaos on a Strange Attractor
- Section 9.4: Lorenz Map
- Section 9.5: Exploring Parameter Space
- Section 9.6: Using Chaos to Send Secret Messages
- Chapter 10: One-Dimensional Maps
- Section 10.1: Fixed Points and Cobwebs
- Section 10.2: Logistic Map: Numerics
- Section 10.3: Logistic Map: Analysis
- Section 10.4: Periodic Windows
- Section 10.5: Liapunov Exponent
- Section 10.6: Universality and Experiments
- Section 10.7: Renormalization
- Chapter 11: Fractals
- Section 11.1: Countable and Uncountable Sets
- Section 11.2: Cantor Set
- Section 11.3: Dimension of Self-Similar Fractals
- Section 11.4: Box Dimension
- Section 11.5: Pointwise and Correlation Dimensions
- Chapter 12: Strange Attractors
- Section 12.1: The Simplest Examples
- Section 12.2: Hénon Maps
- Section 12.3: Rössler Maps
- Section 12.4: Chemical Chaos and Attractor Reconstruction
- Section 12.5: Forced Double-Well Oscillator
| Section 2.1 |
Section 2.2 |
Section 2.3 |
Section 2.4 |
| Problem 2.1.1 |
Problem 2.2.1 |
Problem 2.3.1 |
Problem 2.4.1 |
| Problem 2.1.2 |
Problem 2.2.2 |
Problem 2.3.2 |
Problem 2.4.2 |
| Problem 2.1.3 |
Problem 2.2.3 |
Problem 2.3.3 |
Problem 2.4.3 |
| Problem 2.1.4 |
Problem 2.2.4 |
Problem 2.3.4 |
Problem 2.4.4 |
| Problem 2.1.5 |
Problem 2.2.5 |
Problem 2.3.5 |
Problem 2.4.5 |
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Problem 2.2.6 |
Problem 2.3.6 |
Problem 2.4.6 |
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Problem 2.2.7 |
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Problem 2.4.7 |
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Problem 2.2.8 |
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Problem 2.4.8 |
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Problem 2.2.9 |
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Problem 2.4.9 |
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Problem 2.2.10 |
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Problem 2.2.11 |
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Problem 2.2.12 |
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Problem 2.2.13 |
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| Section 2.5 |
Section 2.6 |
Section 2.7 |
Section 2.8 |
| Problem 2.5.1 |
Problem 2.6.1 |
Problem 2.7.1 |
Problem 2.8.1 |
| Problem 2.5.2 |
Problem 2.6.2 |
Problem 2.7.2 |
Problem 2.8.2 |
| Problem 2.5.3 |
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Problem 2.7.3 |
Problem 2.8.3 |
| Problem 2.5.4 |
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Problem 2.7.4 |
Problem 2.8.4 |
| Problem 2.5.5 |
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Problem 2.7.5 |
Problem 2.8.5 |
| Problem 2.5.6 |
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Problem 2.7.6 |
Problem 2.8.6 |
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Problem 2.7.7 |
Problem 2.8.7 |
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Problem 2.8.8 |
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Problem 2.8.9 |