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微分方程动态系统和混沌导论 第2版PDF|Epub|txt|kindle电子书版本网盘下载
- （美）赫希，斯梅尔著 著
- 出版社： 北京;西安：世界图书出版公司
- ISBN：750628281X
- 出版时间：2007
- 标注页数：417页
- 文件大小：99MB
- 文件页数：40205152页
- 主题词：微分方程－英文；动态系统－英文；混沌学－英文
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图书目录
CHAPTER 1 First-Order Equations1
1.1 The Simplest Example1
1.2 The Logistic Population Model4
1.3 Constant Harvesting and Bifurcations7
1.4 Periodic Harvesting and Periodic Solutions9
1.5 Computing the Poincare Map12
1.6 Exploration：A Two-Parameter Family15
CHAPTER 2 Planar Linear Systems21
2.1 Second-Order Differential Equations23
2.2 Planar Systems24
2.3 Preliminaries from Algebra26
2.4 Planar Linear Systems29
2.5 Eigenvalues and Eigenvectors30
2.6 Solving Linear Systems33
2.7 The Linearity Principle36
CHAPTER 3 Phase Portraits for Planar Systems39
3.1 Real Distinct Eigenvalues39
3.2 Complex Eigenvalues44
3.3 Repeated Eigenvalues47
3.4 Changing Coordinates49
CHAPTER 4 Classification of Planar Systems61
4.1 The Trace-Determinant Plane61
4.2 Dynamical Classification64
4.3 Exploration：A 3D Parameter Space71
CHAPTER 5 Higher Dimensional Linear Algebra75
5.1 Preliminaries from Linear Algebra75
5.2 Eigenvalues and Eigenvectors83
5.3 Complex Eigenvalues86
5.4 Bases and Subspaces89
5.5 Repeated Eigenvalues95
5.6 Genericity101
CHAPTER 6 Higher Dimensional Linear Systems107
6.1 Distinct Eigenvalues107
6.2 Harmonic Oscillators114
6.3 Repeated Eigenvalues119
6.4 The Exponential of a Matrix123
6.5 Nonautonomous Linear Systems130
CHAPTER 7 Nonlinear Systems139
7.1 Dynamical Systems140
7.2 The Existence and Uniqueness Theorem142
7.3 Continuous Dependence of Solutions147
7.4 The Variational Equation149
7.5 Exploration： Numerical Methods153
CHAPTER 8 Equilibria in Nonlinear Systems159
8.1 Some Illustrative Examples159
8.2 Nonlinear Sinks and Sources165
8.3 Saddles168
8.4 Stability174
8.5 Bifurcations176
8.6 Exploration： Complex Vector Fields182
CHAPTER 9 Global Nonlinear Techniques189
9.1 Nullclines189
9.2 Stability of Equilibria194
9.3 Gradient Systems203
9.4 Hamiltonian Systems207
9.5 Exploration： The Pendulum with Constant Forcing210
CHAPTER 10 Closed Orbits and Limit Sets215
10.1 Limit Sets215
10.2 Local Sections and Flow Boxes218
10.3 The Poincare Map220
10.4 Monotone Sequences in Planar Dynamical Systems222
10.5 The Poincare-Bendixson Theorem225
10.6 Applications of Poincare-Bendixson227
10.7 Exploration： Chemical Reactions That Oscillate230
CHAPTER 11 Applications in Biology235
11.1 Infectious Diseases235
11.2 Predator/Prey Systems239
11.3 Competitive Species246
11.4 Exploration： Competition and Harvesting252
CHAPTER 12 Applications in Circuit Theory257
12.1 An RLC Circuit257
12.2 The Lienard Equation261
12.3 The van der Pol Equation262
12.4 A Hopf Bifurcation270
12.5 Exploration： Neurodynamics272
CHAPTER 13 Applications in Mechanics277
13.1 Newton’s Second Law277
13.2 Conservative Systems280
13.3 Central Force Fields281
13.4 The Newtonian Central Force System285
13.5 Kepler’s First Law289
13.6 The Two-Body Problem292
13.7 Blowing Up the Singularity293
13.8 Exploration： Other Central Force Problems297
13.9 Exploration： Classical Limits of Quantum Mechanical Systems298
CHAPTER 14 The Lorenz System303
14.1 Introduction to the Lorenz System304
14.2 Elementary Properties of the Lorenz System306
14.3 The Lorenz Attractor310
14.4 A Model for the Lorenz Attractor314
14.5 The Chaotic Attractor319
14.6 Exploration： The Rossler Attractor324
CHAPTER 15 Discrete Dynamical Systems327
15.1 Introduction to Discrete Dynamical Systems327
15.2 Bifurcations332
15.3 The Discrete Logistic Model335
15.4 Chaos337
15.5 Symbolic Dynamics342
15.6 The Shift Map347
15.7 The Cantor Middle-Thirds Set349
15.8 Exploration： Cubic Chaos352
15.9 Exploration： The Orrbit Diagram353
CHAPTER 16 Homoclinic Phenomena359
16.1 The Shil’nikov System359
16.2 The Horseshoe Map366
16.3 The Double Scroll Attractor372
16.4 Homoclinic Bifurcations375
16.5 Exploration： The Chua Circuit379
CHAPTER 17 Existence and Uniqueness Revisited383
17.1 The Existence and Uniqueness Theorem383
17.2 Proof of Existence and Uniqueness385
17.3 Continuous Dependence on Initial Conditions392
17.4 Extending Solutions395
17.5 Nonautonomous Systems398
17.6 Differentiability of the Flow400
Bibliography407
Index411