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出版社:世界圖書出版公司
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ISBN:9787510095542
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作者:(英)林奇
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頁數:509
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出版日期:2015-05-01
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印刷日期:2015-05-01
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包裝:平裝
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開本:24開
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版次:1
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印次:1
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字數:422千字
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藉助Maple代數操作軟件包,由林奇著的《動力 繫統Maple TM應用(第2版)(英文版)》介紹了動力繫 統的研究原理。作者強調了信息覆蓋面的廣度而不是 細節,而且定理的證明也很少。書中的一些知識點在 別的書中幾乎看不到。常見的定理,如分叉、雙穩定 性、混沌、不穩定性、多穩定性和周期性定理,貫穿 於各章節中。將Maple作為貫穿始終的教學工具,該 書成了數學中的“動手做”教材。 讀者對像:應用數學領域、自然科學和工程類專 業的高年級本科生、研究生和科研工作者。
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Preface 0 A Tutorial Introduction to Maple 0.1 A Quick Tour of Maple 0.2 Tutorial One: The Basics (One Hour) 0.3 Tutorial Two: Plots and Differential Equations (One Hour) 0.4 Simple Maple Programs 0.5 Hints for Programming 0.6 Maple Exercises 1 Differential Equations 1.1 Simple Differential Equations and Applications 1.2 Applications to Chemical Kinetics 1.3 Applications to Electric Circuits 1.4 Existence and Uniqueness Theorem 1.5 Maple Commands 1.6 Exercises 2 Planar Systems 2.1 Canonical Forms. 2.2 Eigenvectors Defining Stable and Unstable Mani/blds 2.3 Phase Portraits of Linear Systems in the Plane 2.4 Linearization and Hartman's Theorem 2.5 Constructing Phase Plane Diagrams 2.6 Maple Commands 2.7 Exercises 3 Interacting Species 3.1 Competing' Species 3.2 Predator-Prey Models 3.3 Other Characteristics Affecting Interacting Species 3.4 Maple Commands 3.5 Exercises 4 Limit Cycles 4.1 Historical Background 4.2 Existence and Uniqueness of Limit Cycles in the Plane 4.3 Nonexistence of Limit Cycles in the Plane 4.4 Perturbation Methods 4.5 Maple Commands 4.6 Exercises 5 Hamiltonian Systems, Lyapunov Functions, and Stability 5.1 Hamiltonian Systems in the Plane 5.2 Lyapunov Functions and Stability 5.3 Maple Commands 5.4 Exercises 6 Bifurcation Theory 6.1 Bifurcations of Nonlinear Systems in the Plane 6.2 Normal Forms 6.3 Multistability and Bistability 6.4 Maple Commands 6.5 Exercises 7 Three-Dimensional Autonomous Systems and Chaos 7.1 Linear Systems and Canonical Forms 7.2 Nonlinear Systems and Stability 7.3 The RSssler System and Chaos 7.4 The Lorenz Equations, Chua's Circuit, and the Belousov-Zhabotinski Reaction 7.5 Maple Commands : 7.6 Exercises 8 Poincare Maps and Nonautonomons Systems in the Plane 8. I Poincar6 Maps 8.2 Hamiltonian Systems with Two Degrees of Freedom 8.3 Nonautonomous Systems in the Plane 8.4 Maple Commands 8.5 Exercises 9 Local and Global Bifurcations 9.1 Small-Amplitude Limit Cycle Bifurcations 9.2 Gr6bner Bases 9.3 Melnikov Integrals and Bifurcating Limit Cycles from a Center 9.4 Bifurcations Involving Homoclinic Loops 9.5 Maple Commands 9.6 Exercises 10 The Second Part of Hilbert's Sixteenth Problem 10.1 Statement of Problem and Main Results 10.2 Poincar6 Compactification 10.3 Global Results for Li6nard Systems 10.4 Local Results for Li~nard Systems 10.5 Exercises 11 Linear Discrete Dynamical Systems 11.1 Recurrence Relations 11.2 The Leslie Model 11.3 Harvesting and Culling Policies 11.4 Maple Commands 11.5 Exercises 12 Nonlinear Discrete Dynamical Systems 12.1 The Tent Map and Graphical Iterations 12.2 Fixed Points and Periodic Orbits 12.3 The Logistic Map, Bifurcation Diagram, and Feigenbaum Number 12.4 Gaussian and H4non Maps 12.5 Applications 12.6 Maple Commands 12.7 Exercises 13 Complex Iterative Maps 13.1 Julia Sets and the Mandelbrot Set 13.2 Boundaries of Periodic Orbits 13.3 Maple Commands 13.4 Exercises 14 Electromagnetic Waves and Optical Resonators 14.1 Maxweil's Equations and Electromagnetic Waves 14.2 Historical Background 14.3 The Nonlinear SFR Resonator 14.4 Chaotic Attractors and Bistability 14.5 Linear Stability Analysis 14.6 Instabilities and Bistability 14.7 Maple Commands 14.8 Exercises 15 Fractals and Multifractals 15.1 Construction of Simple Examples 15.2 Calculating Fractal Dimensions 15.3 A Multifractal Formalism 15.4 Multifractals in the Real World and Some Simple Examples 15.5 Maple Commands 15.6 Exercises 16 Chaos Control and Synchronization 16.1 Historical Background 16.2 Controlling Chaos in the Logistic Map 16.3 Controlling Chaos in the H~non Map 16.4 Chaos Synchronization 16.5 Maple Commands 16.6 Exercises 17 Neural Networks 17.1 Introduction 17.2 The Delta Learning Rule and Backpropagation 17.3 The Hopfield Network and Lyapunov Stability 17.4 Neurodynamics 17.5 Maple Commands 17.6 Exercises 18 Simulation 18.1 Simulink 18.2 The MapleSim Connectivity Toolbox 18.3 MapleSim 18.4 Exercises 19 Examination-Type Questions 19.1 Dynamical Systems with Applications 19.2 Dynamical Systems with Maple 20 Solutions to Exercises 20.0 Chapter 0 20.1 Chapter 1 20.2 Chapter 2 20.3 Chapter 3 20.4 Chapter 4 20.5 Chapter 5 20.6 Chapter 6 20.7 Chapter 7 20.8 Chapter 8 20.9 Chapter 9 20.10 Chapter 10 20.11 Chapter 11 20.12 Chapter 12 20.13 Chapter 13 20.14 Chapter 14 20.15 Chapter 15 20.16 Chapter 16 20.17 Chapter 17 20.18 Chapter 18 20.19 Chapter 19 References Textbooks Research Papers Maple Program Index Index
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