3rd Edition

Student Solutions Manual for Non Linear Dynamics and Chaos With Applications to Physics, Biology, Chemistry, and Engineering

By Mitchal Dichter Copyright 2024
    399 Pages 309 B/W Illustrations
    by CRC Press

    This official Student Solutions Manual includes solutions to the odd-numbered exercises featured in the third 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.

    Part I One-Dimensional Flows

    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

    Part II Two-Dimensional Flows

    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 Poincaré–Bendixson Theorem
    7.4 Liénard 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 Poincaré Maps

    Part III Chaos

    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 Hénon Map
    12.3 Rössler System
    12.4 Chemical Chaos and Attractor Reconstruction
    12.5 Forced Double-Well Oscillator

    Part IV Collective Behavior

    13 Kuramoto Model
    13.1 Governing Equations
    13.2 Visualization and the Order Parameter
    13.3 Mean-Field Coupling and Rotating Frame
    13.4 Steady State
    13.5 Self-Consistency
    13.6 Remaining Questions


    Michael Dichter