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EB

EB

Second edition.

Boulder, CO : Westview Press, a member of the Perseus Books Group, [2015]

1 online zdroj (xiii, \1 s.ges)

ISBN 9780429983276 (e-book: Mobi) (e-book : PDF)

Tištěná verze : ISBN 9780813349107

Obsahuje bibliografické odkazy (pages 470-482) and indexes.

Overview -- One-dimensional flows -- Flows on the line -- Bifurcations -- Flows on the circle -- Two-dimensional flows -- Linear systems -- Phase plane -- Limit cycles -- Bifurcations revisited -- Chaos -- Lorenz equations -- One-dimensional maps -- Fractals -- Strange attractors.

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ENTS // Preface to the Second Edition ix Preface to the First Edition xi // 1 Overview 1 // 1.0 Chaos, Fractals, and Dynamics 1 // 1.1 Capsule History of Dynamics 2 // 1.2 The Importance of Being Nonlinear 4 // 1.3 A Dynamical View of the World 9 // Part I One-Dimensional Flows // 2 Flows on the Line 15 // 2.0 Introduction 15 // 2.1 A Geometric Way of Thinking 16 // 2.2 Fixed Points and Stability 1 // 2.3 Population Growth 21 // 2.4 Linear Stability Analysis 24 // 2.5 Existence and Uniqueness 26 // 2.6 Impossibility of Oscillations 28 // 2.7 Potentials 30 // 2.8 Solving Equations on the Computer 32 Exercises for Chapter 2 36 // 3 Bifurcations 45 // 3.0 Introduction 45 // 3.1 Saddle-Node Bifurcation 46 // 3.2 Transcritical Bifurcation 51 // 3.3 Laser Threshold 54 // 3.4 Pitchfork Bifurcation 56 // 3.5 Overdamped Bead on a Rotating Hoop // 3.6 Imperfect Bifurcations and Catastrophes // 3.7 Insect Outbreak 74 Exercises for Chapter 3 80 // 4 Flows on the Circle 95 // 4.0 Introduction 95 // 4.1 Examples and Definitions 95 // 4.2 Uniform Oscillator 97 // 4.3 Nonuniform Oscillator 98 // 4.4 Overdamped Pendulum 103 // 4.5 Fireflies 105 // 4.6 Superconducting Josephson Junctions 1 // Exercises for Chapter 4 115 // Part II Two-Dimensional Flows // 5 Linear Systems 125 // 5.0 Introduction 125 // 5.1 Definitions and Examples 125 // 5.2 Classification of Linear Systems 131 // 5.3 Love Affairs 139 // Exercises for Chapter 5 142 // 6 Phase Plane 146 // 6.0 Introduction 146 // 6.1 Phase Portraits

146 // 6.2 Existence, Uniqueness, and Topological Consequences 149 // 6.3 Fixed Points and Linearization 151 // 6.4 Rabbits versus Sheep 156 // 6.5 Conservative Systems 160 // 6.6 Reversible Systems 164 // 6.7 Pendulum 168 // 6.8 Index Theory 174 Exercises for Chapter 6 181 // 7 Limit Cycles 198 // 7.0 Introduction 198 // 7.1 Examples 199 // 7.2 Ruling Out Closed Orbits 201 // 7.3 Poincaré-Bendixson Theorem 205 // 7.4 Liénard Systems 212 // 7.5 Relaxation Oscillations 213 // 7.6 Weakly Nonlinear Oscillators 217 Exercises for Chapter 7 230 // 8 Bifurcations Revisited 244 // 8.0 Introduction 244 // 8.1 Saddle-Node, Transcritical, and Pitchfork Bifurcations 244 // 8.2 Hopf Bifurcations 251 // 8.3 Oscillating Chemical Reactions 257 // 8.4 Global Bifurcations of Cycles 264 // 8.5 Hysteresis in the Driven Pendulum and Josephson Junction 268 // 8.6 Coupled Oscillators and Quasiperiodicity 276 // 8.7 Poincaré Maps 281 Exercises for Chapter 8 287 // Part III Chaos // 9 Lorenz Equations 309 // 9.0 Introduction 309 // 9.1 A Chaotic Water wheel 310 // 9.2 Simple Properties of the Lorenz Equations 319 // 9.3 Chaos on a Strange Attractor 325 // 9.4 Lorenz Map 333 // 9.5 Exploring Parameter Space 337 // 9.6 Using Chaos to Send Secret Messages 342 Exercises for Chapter 9 348 // 10 One-Dimensional Maps 355 // 10.0 Introduction 355 // 10.1 Fixed Points and Cobwebs 356 // 10.2 Logistic Map: Numerics 360 // 10.3 Logistic Map: Analysis 364 // 10.4 Periodic Windows 368 // 10.5 Liapunov Exponent

373 // 10.6 Universality and Experiments 376 // 10.7 Renormalization 386 Exercises for Chapter 10 394 // 11 Fractals 405 // 11.0 Introduction 405 // 11.1 Countable and Uncountable Sets 406 // 11.2 Cantor Set 408 // 11.3 Dimension of Self-Similar Fractals 411 // VII // 11.4 Box Dimension 416 // 11.5 Pointwise and Correlation Dimensions 418 Exercises for Chapter 11 423 // 12 Strange Attractors 429 // 12.0 Introduction 429 // 12.1 The Simplest Examples 429 // 12.2 Hénon Map 435 // 12.3 Rössler System 440 // 12.4 Chemical Chaos and Attractor Reconstruction // 12.5 Forced Double-Well Oscillator 447 Exercises for Chapter 12 454 // Answers to Selected Exercises 460 References 470 Author Index 483 Subject Index 487

(OCoLC)1029247331