波卡拉著的《復繫統模型(第2版)(英文版)》旨
在告訴大家復繫統模型是如何建立的，並提供了不可
或缺的工具去研究其動態。然而該書的重點不在於解
釋動態繫統的理論，而是建模，因此呈現給大家的除
了讀者感興趣的信息，還包括動態繫統理論的主要結
論、被忽略掉的技術性很強的定理。盡管動態繫統方
面取得了許多數學進展，例如微分方程和遞推方程，
但是與空間擴展繫統相比，其理論還處在搖籃期。書
中還給出了各學科方面的例證，從生態學到流行病學
，再到社會學，再到地震學。

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