复杂系统动力学：非线性研究

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"dynamics of complex systems" 由 Yaneer Bar-Yam（麻省理工学院学士，博士）撰写，涉及标签包括“混沌”、“神经网络”、“分形”和“复杂系统”。动态复杂系统的研究是现代科学的一个重要领域，它主要关注非线性动力学，即系统的演化和行为如何因初始条件或参数的微小变化而产生显著不同的结果。该领域的研究通常包括混沌理论、神经网络模型、分形几何以及复杂系统分析。混沌理论是理解看似随机但实际上是确定性的系统行为的关键。它探讨了在数学和物理系统中，如何从简单的规则产生出复杂的、不可预测的行为。例如，罗伯特·德凡尼（Robert L. Devaney）的著作如《混沌、分形和动力学：计算机实验》和《非线性动力学和混沌：应用到物理学、生物学、化学和工程》深入浅出地介绍了混沌理论的基础和实际应用。神经网络是模拟人脑神经元工作方式的计算模型，用于解决复杂的学习和决策问题。它们在人工智能、机器学习和模式识别等领域有着广泛的应用。Yaneer Bar-Yam的《复杂系统动力学》可能涉及到神经网络如何在复杂系统中展现其自组织和适应性特性。分形几何是研究不规则形状和结构的数学分支，这些形状在不同尺度上具有自相似性。在混沌系统中，分形经常作为描述边界和吸引子的工具出现。书籍如《经典分形》和《分形之眼》提供了对这一概念的深入了解。复杂系统的研究则超越了单个元素的简单集合，考虑了系统内元素之间的相互作用如何产生整体的复杂行为。这包括生态系统、社会系统和经济系统的复杂性。例如，《混沌动力学软件》和《动力系统软件》可能提供了用于模拟和分析这些复杂系统动态的工具和方法。 "dynamics of complex systems" 是一个涵盖混沌理论、神经网络、分形几何和复杂系统等多个跨学科主题的综合研究，旨在揭示自然界和人造系统中复杂行为的深层次原理。通过这些理论和工具，科学家和工程师能够更好地理解和预测那些看似无序但实际上有内在规律的现象。

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I would like to acknowledge the constructive efforts of the editors at Addison-

Wesley starting from the initial contact with Jack Repcheck and continuing with

Jeff Robbins. I thank Lynne Reed for coordinating production, and at Carlisle

Communications: Susan Steines, Bev Kraus,Faye Schilling, and Kathy Davis.

The software used for the text, graphs, figures and simulations of this book, in-

cludes: Microsoft Excel and Word, Deneba Canvas, Wolfram’s Mathematica, and

Symantec C.The hardware includes:Macintosh Quadra,and IBM RISC workstations.

The contributions of my family, to whom this book is dedicated, cannot be de-

scribed in a few words.

”

Yaneer Bar-Yam

Newton, Massachusetts, June 1997

xvi Ac k n ow l e d g m e n t s

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Overview:

The Dynamics of Complex Systems —

Examples, Questions, Methods and Concepts

The Field of Complex Systems

The study of complex systems in a unified framework has become recognized in re-

cent years as a new scientific discipline, the ultimate of interdisciplinary fields. It is

strongly rooted in the advances that have been made in diverse fields ranging from

physics to anthropology,from which it draws inspiration and to which it is relevant.

Many of the systems that surround us are complex. The goal of understanding

their properties motivates much ifnot all of scientific inquiry.Despite the great com-

plexity and variety of systems, universal laws and phenomena are essential to our in-

quiry and to our understanding. The idea that all matter is formed out of the same

building blocks is one of the original concepts of science.The modern manifestation

of this concept—atoms and their constituent particles—is essential to our recogni-

tion of the commonality among systems in science. The universality of constituents

complements the universality of mechanical laws (classical or quantum) that govern

their motion. In biology, the common molecular and cellular mechanisms of a large

variety oforganisms form the basis of our studies.However,even more universal than

the constituents are the dynamic processes of variation and selection that in some

manner cause organisms to evolve. Thus, all scientific endeavor is based, to a greater

or lesser degree,on the existence of universality,which manifests itself in diverse ways.

In this context,the study of complex systems as a new endeavor strives to increase our

ability to understand the universality that arises when systems are highly complex.

A dictionary definition of the word “complex” is: “consisting of interconnected

or interwoven parts.”Why is the nature of a complex system inherently related to its

parts? Simple systems are also formed out of parts. To explain the difference between

simple and complex systems, the terms “interconnected” or “interwoven”are some-

how essential.Qualitatively,to understand the behavior of a complex system we must

understand not only the behavior of the parts but how they act together to form the

behavior of the whole.It is because we cannot describe the whole without describing

each part, and because each part must be described in relation to other parts, that

complex systems are difficult to understand. This is relevant to another definition of

“complex”:“not easy to understand or analyze.”These qualitative ideas about what a

complex system is can be made more quantitative.Articulating them in a clear way is

0.1

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both essential and fruitful in pointing the way toward progress in understanding the

universal properties of these systems.

For many years, professional specialization has led science to progressive isola-

tion ofindividual disciplines.How is it possible that well-separated fields such as mol-

ecular biology and economics can suddenly become unified in a single discipline?

How does the study of complex systems in general pertain to the detailed efforts de-

voted to the study of particular complex systems? In this regard one must be careful

to acknowledge that there is always a dichotomy between universality and specificity.

A study of universal principles does not replace detailed description of particular

complex systems. However, universal principles and tools guide and simplify our in-

quiries into the study of specifics.For the study of complex systems,universal simpli-

fications are particularly important. Sometimes universal principles are intuitively

appreciated without being explicitly stated. However, a careful articulation of such

principles can enable us to approach particular systems with a systematic guidance

that is often absent in the study of complex systems.

A pictorial way of illustrating the relationship of the field of complex systems to

the many other fields of science is indicated in Fig. 0.1.1. This figure shows the con-

ventional view of science as progressively separating into disparate disciplines in or-

der to gain knowledge about the ever larger complexity of systems.It also illustrates

the view ofthe field of complex systems,which suggests that all complex systems have

universal properties. Because each field develops tools for addressing the complexity

of the systems in their domain, many of these tools can be adapted for more general

use by recognizing their universal applicability. Hence the motivation for cross-

disciplinary fertilization in the study of complex systems.

In Sections 0.2–0.4 we initiate our study of complex systems by discussing ex-

amples,questions and methods that are relevant to the study ofcomplex systems.Our

purpose is to introduce the field without a strong bias as to conclusions, so that the

student can develop independent perspectives that may be useful in this new field—

opening the way to his or her own contributions to the study of complex systems. In

Section 0.5 we introduce two key concepts—emergence and complexity—that will

arise through our study of complex systems in this text.

Examples

0.2.1 A few examples

What are com p l e x sys tems and what properties ch a racteri ze them? It is hel pful to start

by making a list ofs ome examples ofcom p l ex sys t em s .Ta ke a few minutes to make yo u r

own list. Con s i der actual sys tems ra t h er than mathem a tical models (we wi ll con s i der

m a t h em a t ical models later ) .Ma ke a list of s ome simple things to con trast them wi t h .

Examples of Complex Systems

Governments

Families

The human body—physiological perspective

0.2

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A person—psychosocial perspective

The brain

The ecosystem of the world

Subworld ecosystems: desert,rain forest,ocean

Weather

A corporation

A computer

Examples of Simple Systems

An oscillator

A pendulum

A spinning wheel

An orbiting planet

The purpose of thinking about examples is to develop a first understanding of the

question,What makes systems complex? To begin to address this question we can start

describing systems we know intuitively as complex and see what properties they share.

We try this with the first two examples listed above as complex systems.

Government

• It has many different functions:military, immigration,taxation,income distrib-

ution,transportation, regulation.Each function is itself complex.

• There are different levels and types of government: local, state and federal; town

meeting, council,mayoral. There are also various governmental forms in differ-

ent countries.

Family

• It is a set of individuals.

• Each individual has a relationship with the other individuals.

• Th ere is an interp l a y bet ween the rel a ti onship and the qu a l i ties of the indivi du a l .

• The family has to interact with the outside world.

• There are different kinds of families:nuclear family, extended family, etc.

These descriptions focus on function and structure and diverse manifestation.

We can also consider the role that time plays in complex systems.Among the proper-

ties of complex systems are change,growth and death,possibly some form of life cy-

cle. Combining time and the environment, we would point to the ability of complex

systems to adapt.

One of the issues that we will need to address is whether there are different cate-

gories of complex systems. For example, we might contrast the systems we just de-

scribed with complex physical systems: hydrodynamics (fluid flow,weather), glasses,

composite materials, earthquakes.In what way are these systems similar to or differ-

ent from the biological or social complex systems? Can we assign function and discuss

structure in the same way?

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