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[资源] It's a Nonlinear World

Preface xi
Part I: WORLD OF MATHEMATICS 1
1 World of Nonlinear Systems
1.1 Introduction to Nonlinear ODE Models
1.2 Introduction to Difference Equation Models
1.3 Solving Nonlinear ODEs on the Computer ..
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2 World of Nonlinear ODEs
2.1 Breakdown of Linear Superposition.
2.2 Some Analytically Solvable Examples .
2.3 Fixed Points and Phase-Plane Analysis ..
2.4 Bifurcations .
2.5 Hysteresis and the Jump Phenomena ..
2.6 Limit Cycles .
2.7 Strange Attractors and Chaos .
2.8 Fractal Dimensions . . .
2.9 Poincare Sections .
2.10 Power Spectrum .. . .
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Fixed Points of One-Dimensional Maps .
Stability Criterion . . . . . . . . . .
Cobweb Diagram. . . . . . . ....
Period Doubling to Chaos . . . . . .
Creating Lorenz Maps. ... . .
Lyapunov Exponent . . . . . . . . .
Two-Dimensional Maps .. . . . . .
Mandelbrot and Julia Sets .
Chaos versus Noise . . . . . .
Controlling Chaos .
3 World of Nonlinear Maps
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
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viii CONTENTS
4 World of Solitons
4.1 Korteweg-deVries Solitons ..
4.2 Sine-Gordon Solitons . . . . . . . . . . . . . . . . . .
4.3 Similarity Solutions. . . . .
4.4 Numerical Simulation ...
4.4.1 Finite Difference Approximations ..
4.4.2 The Zabusky-Kruskal Algorithm . .
4.4.3 Method of Characteristics .
4.4.4 Numerical Algorithm for the SGE .
4.4.5 Numerical Stability. . . . . . . . .
4.5 Extension to Cellular Automata .
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Part II: OUR NONLINEAR WORLD 129
5 World of Motion
5.1 Nonlinear Drag or Resistance .
5.2 Nonlinear Lift .
5.3 The Pendulum, Simple and Otherwise
5.3.1 The Simple Pendulum .
5.3.2 Parametric Excitation .
5.3.3 The Rotating Pendulum . .
5.4 Nonlinear Springs .
5.4.1 Lattice Dynamics .
5.5 Hysteresis and Jumps Revisited .
5.6 Precession of Mercury . . . . . .
5.7 Saturn's Rings: A "Toy" Model.
5.8 Hamiltonian Chaos .
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The Aerodynamics of Sports Balls . . . . .
Bend It Like Beckham ...
A Major League Curveball .
Golf Ball Trajectory . . . .
A Falling Badminton Bird .
Car Racing ....
Medieval Archery . . . . . . . . . . .
6 World of Sports
6.1
6.2
6.3
6.4
6.5
6.6
6.7
7 World of Electromagnetism
7.1 Nonlinear Electrical Circuits. . . . . . . . .
7.1.1 Nonlinear Inductance .
7.1.2 Nonlinear Capacitance . . .
7.1.3 Chua's Circuit: Piecewise-Linear Negative Resistance
7.1.4 Tunnel Diode Oscillator .
7.1.5 Josephson Junction .
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CONTENTS ix
7.1.6 SQUID Magnetometer. . . . . . . . . . . . . . . .... . 208
7.2 Nonlinear Optics . . . . . . . . . .. . . . . . . . . . . .. 209
7.2.1 Optical Soliton Propagation. . . . . . . . . . . . . . . 210
7.2.2 The Navier-Stokes Equations . . . . . . .. 213
7.2.3 Stimulated Scattering of Light 216
7.3 The Earth's Magnetic Field . . . . . . . . . . . . . . . . . . . .. 218
7.3.1 Aurora Borealis. . . . . . . . . . . . . . . . 218
7.3.2 The Drifting North Magnetic Pole . . . . . . . . . . . 221
7.3.3 The Geodynamo Origin of the Earth's Magnetic Field 222
8 World of Weather Prediction
8.1 Early History .
8.2 The Barotropic Vorticity Equation
8.3 Some Meteorological Concepts ...
8.4 Modern Numerical Weather Forecasting
9 World of Chemistry
9.1 Chemical Reactions .
9.1.1 Autocatalysis .
9.1.2 Michaelis-Menten Enzyme Kinetics ..
9.1.3 Lotka-Volterra Mechanism
9.2 Chemical Oscillators .. . .
9.2.1 The Oregonator .
9.2.2 The Brusselator .
9.3 Chemical Waves and Patterns .
9.3.1 Target Patterns and Spiral Waves .
9.3.2 Reaction-Diffusion Equations .
9.3.3 How the Leopard Got Its Spots .
10 World of Disease
10.1 Classifying the Spread of Infectious Diseases ..
10.2 Basic Models of Disease Transmission .
10.2.1 The SIS Model .
10.2.2 The SIR Model without Vital Dynamics .
10.2.3 The SIR Model with Vital Dynamics .
10.2.4 Herd Immunity and Vaccination .. . .
10.2.5 Geographic Spread of an Epidemic . . . . . . . . . . . . . . . . .
10.3 Examples of Disease Growth . .
10.3.1 Mad Cow Disease. . . . . . . .
10.3.2 Avascular Tumor Growth . . . . . . . . . .
11 World of War
11.1 The Coevolutionary Arms Race .
11.1.1 The Newt versus the Garter Snake. . . . . . . . .
11.1.2 Biological Arms Race with a Dangerous Prey .....
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x CONTENTS
11.1.3 The Wild Parsnip and Geographic Mosaic Theory .
11.2 Human Conflict .
11.2.1 Political Complexity: Nonlinear Models of Politics
11.2.2 Richardson Arms Race Model .
11.2.3 Chaos-a Model for the Outbreak of War .
11.2.4 The Dynamics of Warfare: Lanchester Equations
11.2.5 War of the Fire Ants .
Bibliography
Index
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