- 复系统模型(第2版)(英文版)
- - 作者：(美)波卡拉
  - 出版社：世界图书出版公司
  - ISBN：9787510095597
  - 出版日期：2015/05/01
  - 页数：489
- 售价：31.2

内容大纲
波卡拉著的《复系统模型(第2版)(英文版)》旨在告诉大家复系统模型是如何建立的，并提供了不可或缺的工具去研究其动态。然而该书的重点不在于解释动态系统的理论，而是建模，因此呈现给大家的除了读者感兴趣的信息，还包括动态系统理论的主要结论、被忽略掉的技术性很强的定理。尽管动态系统方面取得了许多数学进展，例如微分方程和递推方程，但是与空间扩展系统相比，其理论还处在摇篮期。书中还给出了各学科方面的例证，从生态学到流行病学，再到社会学，再到地震学。
作者介绍
目录
Preface of the First Edition
Preface of the Second Edition
Notations
1 Introduction
  1.1 What is a Complex System？
  1.2 What is a Model？
  1.3 What is a Dynamical System？
  Exercises
  Solutions
  Summary
2 How to Build Up a Model
  2.1 Lotka—Volterra Model
  2.2 More R，ealistic Predator—Prey Models
  2.3 A Model with a Stable Limit Cycle
  2.4 Fluctuating Environments
  2.5 Hutchinson's Time—Delay Model
  2.6 Discrete—Time Models
  2.7 Lattice Models
  Exercises
  Solutions
  Summary
3 Differential Equations
  3.1 Flows
  3.2 Linearization and Stability
    3.2.1 Linear Systems
    3.2.2 Nonlinear Systems
  3.3 Graphical Study of Two—Dimensional Systems
  3.4 Structural Stability
  3.5 Local Bifurcations of Vector Fields
    3.5.1 One—Dimensional Vector Fields
    3.5.2 Equivalent Families of Vector Fields
    3.5.3 Hopf Bifurcation
    3.5.4 Catastrophes
  3.6 Influence of Diffusion
    3.6.1 Random Walk and Diffusion
    3.6.2 One—Population Dynamics with Dispersal
    3.6.3 Critical Patch Size
    3.6.4 Diffusion—Induced Instability
  Exercises
  Solutions
  Summary
4 Recurrence Equations
  4.1 Iteration of Maps
  4.2 Stability
  4.3 Poincare Maps
  4.4 Local Bifurcations of Maps
    4.4.1 Maps on R
    4.4.2 The Hopf Bifurcation
  4.5 Sequences of Period—Doubling Bifurcations
    4.5.1 Logistic Model

    4.5.2 Universality
  Exercises
  Solutions
  Summary
5 Chaos
  5.1 Defining Chaos
    5.1.1 Dynanucs of the Logistic Map f4
    5.1.2 Definition of Chaos
  5.2 Routes to Chaos
  5.3 Characterizing Chaos
    5.3.1 Stochastic Properties
    5.3.2 Lyapunov Exponent
    5.3.3 "Period Threelmplies Chaos"
    5.3.4 Strange Attractors
  5.4 Chaotic Discrete—Time Models
    5.4.1 One—Population Models
    5.4.2 The Henon Map
  5.5 Chaotic Continuous—Time Models
    5.5.1 The Lorenz Model
  Exercises
  Solutions
  Summary
6 Spatial Models
  6.1 Cellular Automata
  6.2 Number—Conserving Cellular Automata
  6.3 Eventually Number—Conserving Cellular Automata
  6.4 Approximate Methods
  6.5 Generalized Cellular Automata
  6.6 Kinetic Growth Phenomena
  6.7 Site—Exchange Cellular Automata
  6.8 Agent—Based Spatial Models
  6.9 Sociophysics
  Exercises
  Solutions
  Summary
7 Networks
  7.1 The Small—World Phenomenon
  7.2 Graphs
  7.3 Random Networks
  7.4 Small—World Networks
    7.4.1 Watts—Strogatz Model
    7.4.2 Newman—Watts Model
    7.4.3 Highly Connected Extra Vertex Model
  7.5 Scale—Free Networks
    7.5.1 Empirical Results
    7.5.2 A Few Models
  Exercises
  Solutions
  Summary
8 Power—Law Distributions

  8.1 Classical Examples
  8.2 A Few Notions of Probability Theory
    8.2.1 Basic Definitions
    8.2.2 Central Limit Theorem
    8.2.3 Lognormal Distribution
    8.2.4 Levy Distributions
    8.2.5 Truncated Levy Distributions
    8.2.6 Student's t—Distribution
    8.2.7 A Word About Statistics
  8.3 Empirical Results and Tentative Models
    8.3.1 Financial Markets
    8.3.2 Demographic and Area Distribution
    8.3.3 Family Names
    8.3.4 Distribution of Votes
  8.4 Self—Organized Criticality
    8.4.1 The Sandpile Model
    8.4.2 Drossel—Schwabl Forest Fire Model
    8.4.3 Punctuated Equilibria and Darwinian Evolution
    8.4.4 Real— Life Phenomena
  Exercises
  Solutions
  Summary
Glossary
References
Index

内容大纲

作者介绍

目录

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