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微分方程動態系統和混沌導論（第2版） 版權信息
- ISBN：9787506282819
- 條形碼：9787506282819 ; 978-7-5062-8281-9
- 裝幀：一般膠版紙
- 冊數：暫無
- 重量：暫無
- 所屬分類：>>
微分方程動態系統和混沌導論（第2版） 本書特色
本書是30年前世界著名的動力系統專家赫希(M．Hirsch)和斯梅爾(S．Smale)合著的“Differential Equations，Dynamical Systems and Linear Algebra”一書的修訂本，原書初版后被許多高校作為動力系統入門的標準教材，多年來在國際上產生較大影響。
微分方程動態系統和混沌導論（第2版） 內容簡介
30年來，動力系統的數學理論與應用有了很大發展。30多年前還沒有高速的臺式計算機和計算機圖像，“混沌”一詞也沒有在數學界使用，而對于微分方程與動力系統的研究興趣主要僅限于數學界中比較小的范圍。到今天，處處有計算機，求微分方程近似解的軟件包已得到廣泛運用，使人們從圖形中就能看到結果。對于非線性微分方程的分析已為廣大學者所接受，一些復雜的動力學行為，如馬蹄映射、同宿軌、Lorenz系統中揭示出來的復雜現象，以及數學方面的分析，使學者們確信簡單的穩定運動，如平衡態和周期解己不總是微分方程解的*重要的行為，而混沌現象揭示出來的美妙性態正促使各個領域的科學家與工程師細心關注在他們自己領域中提出的重要的微分方程及其混沌特性。動力系統現象在今天已出現在幾乎每個科學領域中，從化學中的振蕩Belousov-Zhabotinsky反應到電子工程中的混沌Chua電路，從天體力學中的復雜運動到生態系統中的分岔。
微分方程動態系統和混沌導論（第2版） 目錄
CHAPTER 1 First-Order Equations
1.1 The Simplest Example
1.2 The Logistic Population Model
1.3 Constant Harvesting and Bifurcations
1.4 Periodic Harvesting and Periodic Solutions
1.5 Computing the Poincard Map
1.6 Exploration：A Two-Parameter Family
CHAPTER 2 Planar Linear Systems
2.1 Second-Order Differential Equations
2.2 Planar Systems
2.3 Preliminaries from Algebra
2.4 Planar Linear Systems
2.5 Eigenvalues and Eigenvectors
2.6 Solving Linear Systems
2.7 The Linearity Principle
CHAPTER 3 Phase Portraits for Planar Systems
3.1 Real Distinct Eigenvalues
3.2 Complex Eigenvalues
3.3 Repeated Eigenvalues
3.4 Changing Coordinates
CHAPTER 4 Classification of Planar Systems
4.1 The Trace-Determinant Plane
4.2 Dynamical Classification
4.3 Exploration：A 3D Parameter Space
CHAPTER 5 Higher Dimensional Linear Algebra
5.1 Preliminaries from Linear Algebra
5.2 Eigenvalues and Eigenvectors
5.3 Complex Eigenvalues
5.4 Bases and Subspaces
5.5 Repeated Eigenvalues
5.6 Genericity
CHAPTER 6 Higher Dimensional Linear Systems
6.1 Distinct Eigenvalues
6.2 Harmonic Oscillators
6.3 Repeated Eigenvalues
6.4 The Exponential of a Matrix
6.5 Nonautonomous Linear Systems
CHAPTER 7 Nonlinear Systems
7.1 Dynamical Systems
7.2 The Existence and Uniqueness Theorem
7.3 Continuous Dependence of Solutions
7.4 The Variational Equation
7.5 Exploration：Numerical Methods
CHAPTER 8 Equilibria in Nonlinear Systems
8.1 Some Nustrative Examples
8.2 Nonlinear Sinks and Sources
8.3 Saddles
8.4 Stability
8.5 Bifurcations
8.6 Exploration：Complex Vector Fields
CHAPTER 9 Global Nonlinear Techniques
9.1 Nullclines
9.2 Stability of Equilibria
9.3 Gradient Systems
9.4 Hamiltonian Systems
9.5 Exploration：The Pendulum with Constant Forcing
CHAPTER 10 Closed Orbits and Limit Sets
10.1 Limit Sets
10.2 Local Sections and Flow Boxes
10.3 The Poincare Map
10.4 Monotone Sequences in Planar Dynamical Systems
10.5 The Poincare-Bendixson Theorem
10.6 Applications of Poincare-Bendixson
10.7 Expl0ration：Chemical Reactions That Oscillate
CHAPTER 11 Applications in Biology
11.1 Infectious Diseases
11.2 Predator／Prey Systems
11.3 Competitive Species
11.4 Exploration：Competition and Harvesting
CHAPTER 12 Applications in Circuit Theory
12.1 An RLC Circuit
12.2 The Lienard Equation
12.3 The van der Pol Equation
12.4 A Hopf Bifurcation
12.5 Exploration：Neurodynamics
CHAPTER 13 Applications in Mechanics
13.1 Newton’S Second Law
13.2 Conservative Systems
13.3 Central Force Fields
13.4 The Newtonian Central Force System
13.5 Kepler’s First Law
13.6 The Two-Body Problem
13.7 Blowing Up the Singularity
13.8 Exploration：Other Central Force Problems
13.9 Exploration：Classical Limits of Quantum Mechanical Systems
CHAPTER 14 The Lorenz System
14.1 Introduction to the Lorenz System
14.2 Elementary Properties of the Lorenz System
14.3 The Lorenz Attractor
14.4 A Model for the Lorenz Attractor
14.5 The Chaotic Attractor
14.6 Exploration：The Rossler Attractor
CHAPTER 15 Discrete Dynamical Systems
15.1 Introduction to Discrete Dynamical Systems
15.2 Bifurcations
15.3 The Discrete Logistic Model
15.4 Chaos
15.5 Symbolic Dynamics
15.6 The Shift Map
15.7 The Cantor Middle-Thirds Set
15.8 Exploration：Cubic Chaos
15.9 Exploration：The Orbit Diagram
CHAPTER 16 Homoclinic Phenomena
16.1 The Shil’nikov System
16.2 The Horseshoe Map
16.3 The Double Scroll Attractor
16.4 Homoclinic Bifurcations
16.5 Exploration：The Chua Circuit
CHAPTER 17 Existence and Uniqueness Revisited
17.1 The Existence and Uniqueness Theorem
17.2 Proof of Existence and Uniqueness
17.3 Continuous Dependence on Initial Conditions
17.4 Extending Solutions
17.5 Nonautonomous Systems
17.6 Differentiability of the Flow
Bibliography
Index
1.1 The Simplest Example
1.2 The Logistic Population Model
1.3 Constant Harvesting and Bifurcations
1.4 Periodic Harvesting and Periodic Solutions
1.5 Computing the Poincard Map
1.6 Exploration：A Two-Parameter Family
CHAPTER 2 Planar Linear Systems
2.1 Second-Order Differential Equations
2.2 Planar Systems
2.3 Preliminaries from Algebra
2.4 Planar Linear Systems
2.5 Eigenvalues and Eigenvectors
2.6 Solving Linear Systems
2.7 The Linearity Principle
CHAPTER 3 Phase Portraits for Planar Systems
3.1 Real Distinct Eigenvalues
3.2 Complex Eigenvalues
3.3 Repeated Eigenvalues
3.4 Changing Coordinates
CHAPTER 4 Classification of Planar Systems
4.1 The Trace-Determinant Plane
4.2 Dynamical Classification
4.3 Exploration：A 3D Parameter Space
CHAPTER 5 Higher Dimensional Linear Algebra
5.1 Preliminaries from Linear Algebra
5.2 Eigenvalues and Eigenvectors
5.3 Complex Eigenvalues
5.4 Bases and Subspaces
5.5 Repeated Eigenvalues
5.6 Genericity
CHAPTER 6 Higher Dimensional Linear Systems
6.1 Distinct Eigenvalues
6.2 Harmonic Oscillators
6.3 Repeated Eigenvalues
6.4 The Exponential of a Matrix
6.5 Nonautonomous Linear Systems
CHAPTER 7 Nonlinear Systems
7.1 Dynamical Systems
7.2 The Existence and Uniqueness Theorem
7.3 Continuous Dependence of Solutions
7.4 The Variational Equation
7.5 Exploration：Numerical Methods
CHAPTER 8 Equilibria in Nonlinear Systems
8.1 Some Nustrative Examples
8.2 Nonlinear Sinks and Sources
8.3 Saddles
8.4 Stability
8.5 Bifurcations
8.6 Exploration：Complex Vector Fields
CHAPTER 9 Global Nonlinear Techniques
9.1 Nullclines
9.2 Stability of Equilibria
9.3 Gradient Systems
9.4 Hamiltonian Systems
9.5 Exploration：The Pendulum with Constant Forcing
CHAPTER 10 Closed Orbits and Limit Sets
10.1 Limit Sets
10.2 Local Sections and Flow Boxes
10.3 The Poincare Map
10.4 Monotone Sequences in Planar Dynamical Systems
10.5 The Poincare-Bendixson Theorem
10.6 Applications of Poincare-Bendixson
10.7 Expl0ration：Chemical Reactions That Oscillate
CHAPTER 11 Applications in Biology
11.1 Infectious Diseases
11.2 Predator／Prey Systems
11.3 Competitive Species
11.4 Exploration：Competition and Harvesting
CHAPTER 12 Applications in Circuit Theory
12.1 An RLC Circuit
12.2 The Lienard Equation
12.3 The van der Pol Equation
12.4 A Hopf Bifurcation
12.5 Exploration：Neurodynamics
CHAPTER 13 Applications in Mechanics
13.1 Newton’S Second Law
13.2 Conservative Systems
13.3 Central Force Fields
13.4 The Newtonian Central Force System
13.5 Kepler’s First Law
13.6 The Two-Body Problem
13.7 Blowing Up the Singularity
13.8 Exploration：Other Central Force Problems
13.9 Exploration：Classical Limits of Quantum Mechanical Systems
CHAPTER 14 The Lorenz System
14.1 Introduction to the Lorenz System
14.2 Elementary Properties of the Lorenz System
14.3 The Lorenz Attractor
14.4 A Model for the Lorenz Attractor
14.5 The Chaotic Attractor
14.6 Exploration：The Rossler Attractor
CHAPTER 15 Discrete Dynamical Systems
15.1 Introduction to Discrete Dynamical Systems
15.2 Bifurcations
15.3 The Discrete Logistic Model
15.4 Chaos
15.5 Symbolic Dynamics
15.6 The Shift Map
15.7 The Cantor Middle-Thirds Set
15.8 Exploration：Cubic Chaos
15.9 Exploration：The Orbit Diagram
CHAPTER 16 Homoclinic Phenomena
16.1 The Shil’nikov System
16.2 The Horseshoe Map
16.3 The Double Scroll Attractor
16.4 Homoclinic Bifurcations
16.5 Exploration：The Chua Circuit
CHAPTER 17 Existence and Uniqueness Revisited
17.1 The Existence and Uniqueness Theorem
17.2 Proof of Existence and Uniqueness
17.3 Continuous Dependence on Initial Conditions
17.4 Extending Solutions
17.5 Nonautonomous Systems
17.6 Differentiability of the Flow
Bibliography
Index
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