非线性工作手册：应用C++、Java 与符号C++程序的浑沌、分形、细胞自动机、神经网络、遗传算法、基因表达编程、支持向量机、子波、隐马可NONLINEAR WORKBOOK, THE
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作者： Willi-Hans Steeb 著
出 版 社： Penguin
出版时间： 1999-12-1字数：版次： 1页数： 585印刷时间： 1999/11/01开本：印次：纸张： 胶版纸I S B N ： 9789810240257包装： 精装内容简介
The study of nonlinear dynamical systems has advanced tremendously in the last 20 years, making a big impact on science and technology. This book provides all the techniques and methods used in nonlinear dynamics. The concepts and underlying mathematics are discussed in detail.
The numerical and symbolic methods are implemented in C++, SymbolicC++ and Java. Object-oriented techniques are also applied. The book contains more than 150 ready-to-run programs.
The text has also been designed for a one-year course at both the junior and senior levels in nonlinear dynamics. The topics discussed in the book are part of e-learning and distance learning courses conducted by the International School for Scientific Computing.
目录
Preface
1 Nonlinear and Chaotic Maps
1.1 One-Dimensional Maps
1.1.1 Exact and Numerical Trajectories
1.1.2 Fixed Points and Stability
1.1.3 Invariant Density
1.1.4 Liapunov Exponent
1.1.5 Autocorrelation Function
1.1.6 Discrete Fourier Transform
1.1.7 Fast Fourier Transform
1.1.8 Logistic Map and Liapunov Exponent for r C [3,4]
1.1.9 Logistic Map and Bifurcation Diagram
1.1.10 Random Number Map and Invariant Density
1.1.11 Random Number Map and Random Integration . . .
1.1.12 Circle Map and Rotation Number
1.1.13 Newton Method
1.1.14 Feigenbaum's Constant
1.1.15 Symbolic Dynamics
1.2 Two-Dimensional Maps
1.2.1 Introduction
1.2.2 Phase Portrait
1.2.3 Fixed Points and Stability
1.2.4 Liapunov Exponents
1.2.5 Correlation Integral
1.2.6 Capacity
1.2.7 Hyperchaos
1.2.8 Domain of Attraction
1.2.9 Newton Method in the Complex Domain
1.2.10 Newton Method in Higher Dimensions
1.2.11 Ruelle-Takens-Newhouse Scenario
2 Time Series Analysis
2.1 Introduction
2.2 Correlation Coefficient
2.3 Liapunov Exponent from Time Series
2.3.1 Jacobian Matrix Estimation Algorithm
2.3.2 Direct Method
2.4 Hurst Exponent
2.4.1 Introduction
2.4.2 Algorithm for the Hurst Exponent
2.5 Complexity
3 Autonomous Systems in the Plane
3.1 Classification of Fixed Points
3.2 Homoclinic Orbit
3.3 Pendulum
3.4 Limit Cycle Systems
3.5 Lotka-Volterra Systems
4 Nonlinear Hamilton Systems
4.1 Hamilton Equations of Motion
4.1.1 Hamilton System and Variational Equation
4.2 Integrable Hamilton Systems
4.2.1 Hamilton Systems and First Integrals
4.2.2 Lax Pair and Hamilton Systems
4.2.3 Floquet Theory
4.3 Chaotic Hamilton Systems
4.3.1 H@non-Heiles Hamilton Function and Trajectories . . .
4.3.2 H@non-Heiles and Surface of Section Method
4.3.3 Quartic Potential and Surface of Section Technique . .
5 Nonlinear Dissipative Systems
5.1 Fixed Points and Stability
5.2 Trajectories
5.3 Phase Portrait
5.4 Liapunov Exponents
5.5 Generalized Lotka-Volterra Model
5.6 Hyperchaotic Systems
5.7 Hopf Bifurcation
5.8 Time-Dependent First Integrals
6 Nonlinear Driven Systems
6.1 Introduction
6.2 Driven Anharmonic Systems
6.2.1 Phase Portrait
6.2.2 Poincare Section
6.2.3 Liapunov Exponent
6.2.4 Autocorrelation Function
6.2.5 Power Spectral Density
6.3 Driven Pendulum
6.3.1 Phase Portrait
……
7 Controlling and Synchronization of Chaos
8 Fractals
9 Cellular Automata
10 Solving Differential Equations
11 Neural Networks
12 Genetic Algorithms
13 Fuzzy Sets and Fuzzy Logic
Bibliography
Index
