Systems science

390 Pages·14.053 MB·English

by  Politechnika Wrocławska

Systems and Control Engineering L Systems Science
Z
i
hn
By making use of the principles of systems science, the scientific community can explain many a
o•
complicated matters of the world and shed new light on unsettled problems. Each real science

has its own particular methodology for not only qualitative but also quantitative analyses, so it •D
u
is important to understand the organic whole of systems research with operable mathematical X
a
methods. Systems Science: Methodological Approaches presents a mathematical explanation un Methodological Approaches
of systems science, giving readers a complete technical formulation of different systemic laws.
It enables them to use a unified methodology to attack different problems that are hard, if not
impossible, for modern science to handle.
Following a brief history of systems science, the book explores:
S
• Basic concepts, characteristics, properties, and classifications of general systems
y
• Nonlinear systems dynamics and the theory of catastrophe
• Dissipative structures and synergistics s
• Studies of chaos, including logistic mapping, phase space reconstruction, t
Lyapunov exponents, and chaos of general single relation systems
e
• Different aspects and concepts of fractals, including a presentation of L systems
analysis and design m
• Complex systems and complexity, with a discussion of how the phenomena of
“three” and complexity are related, and how various cellular automata can be
constructed to generate useful simulations and figurative patterns s
• Complex adaptive systems and open complex giant systems, with an introduction
to the yoyo model and practical applications
S
• Complex networks and related concepts and methods
c
The book concludes with several case studies that demonstrate how various concepts and the
i
logic of systems can be practically applied to resolve real-life problems, such as the prediction
e
of natural disasters. The book will be useful in directing future research and applications of
systems science on a commonly accepted platform and playground.
n
c
e Yi Lin
Xiaojun Duan
K14233
ISBN: 978-1-4398-9551-1
Chengli Zhao
90000
www.crcpress.com
9 781439 895511 Lida Xu
w w w.c r c p r e s s .co m
K14233 cvr mech.indd 1 10/9/12 9:23 AM
Systems Science
Methodological Approaches
Advances in Systems Science and Engineering
Series Editor: Lida Xu
PubliShEd
Systems Science: Methodological Approaches
by Yi Lin, Xiaojun Duan, Chengli Zhao, and Lida Xu
ISBN: 978-1-4398-9551-1
forthcoming
Enterprise Integration and Information Architecture:
A Systems Perspective on Industrial Information Integration
by Lida Xu
ISBN: 978-1-4398-5024-4
Systems Science
Methodological Approaches
Yi Lin
Xiaojun Duan
Chengli Zhao
Lida Xu
MATLAB® is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks does not warrant the
accuracy of the text or exercises in this book. This book’s use or discussion of MATLAB® software or related products
does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular
use of the MATLAB® software.
CRC Press
Taylor & Francis Group
6000 Broken Sound Parkway NW, Suite 300
Boca Raton, FL 33487-2742
© 2013 by Taylor & Francis Group, LLC
CRC Press is an imprint of Taylor & Francis Group, an Informa business
No claim to original U.S. Government works
Version Date: 20121030
International Standard Book Number-13: 978-1-4398-9552-8 (eBook - PDF)
This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been
made to publish reliable data and information, but the author and publisher cannot assume responsibility for the valid-
ity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright
holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this
form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may
rectify in any future reprint.
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or uti-
lized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopy-
ing, microfilming, and recording, or in any information storage or retrieval system, without written permission from the
publishers.
For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://
www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923,
978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For
organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged.
Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for
identification and explanation without intent to infringe.
Visit the Taylor & Francis Web site at
http://www.taylorandfrancis.com
and the CRC Press Web site at
http://www.crcpress.com
Contents
Preface............................................................................................................................................xiii
Acknowledgments ..........................................................................................................................xvii
Authors ............................................................................................................................................xix
Chapter 1 A Brief History of Systems Science .............................................................................1
1.1 What Is Systems Science? .................................................................................1
1.2 Development History of Systems Science .........................................................2
1.2.1 Formation of Systemic Thoughts—The Elementary Stage..................3
1.2.2 Quantitative Systems Science Developed for Applications .................6
1.2.3 Construction of Comprehensive Systems Science .............................10
1.3 System of Modern Science and Technology ...................................................12
1.4 Disciplinary Characteristics of Systems Science ............................................15
1.4.1 Schools of Systemic Thought .............................................................16
1.4.2 Suggestions from World of Learning .................................................16
1.5 Some Philosophical Thoughts of Systems Science .........................................17
1.6 Philosophical Significance of Systemic Epistemology ...................................18
1.6.1 Ludwig von Bertalanffy .....................................................................18
1.6.2 Ilya Prigogine .....................................................................................19
1.6.3 Hermann Haken .................................................................................20
1.6.4 Manfred Eigen ....................................................................................20
1.6.5 James Grier Miller .............................................................................21
1.6.6 Qian Xuesen .......................................................................................21
1.6.7 Sunny Y. Auyang ................................................................................21
1.6.8 Others .................................................................................................21
1.7 Some Unsettled Questions ...............................................................................21
1.7.1 Are Systems Thoughts Commonly Usable Scientific Views? ............21
1.7.2 Can Systems Research Help with the Understanding of
Complex Systems? ..............................................................................22
1.8 Organization of This Book ..............................................................................22
1.9 Open-Ended Problems .....................................................................................22
Chapter 2 Concepts, Characteristics, and Classifications of Systems ........................................23
2.1 Fundamental Concepts ....................................................................................23
2.1.1 Systems and Nonsystems ...................................................................23
2.1.2 Components, Elements, and Factors ..................................................26
2.1.3 Structures and Subsystems .................................................................27
2.1.4 Levels .................................................................................................29
2.1.5 Environments .....................................................................................30
2.2 Properties of Systems ......................................................................................32
2.2.1 Additive and Combinatorial Wholeness.............................................32
2.2.2 Holistic Emergence of Systems ..........................................................34
2.2.2.1 Holistic Emergence .............................................................34
2.2.2.2 Scales and Emergence ........................................................34
v
vi Contents
2.2.2.3 Structures, Levels, and Emergence .....................................34
2.2.2.4 Environments and Emergence ............................................35
2.2.3 Other Properties of Systems ...............................................................37
2.2.4 Functionalities of Systems ..................................................................37
2.2.5 Attributes of Systems .........................................................................38
2.3 Dynamics and Time Systems ..........................................................................40
2.4 Classification of Systems .................................................................................41
2.4.1 Nonsystems Scientific Classification of Systems ...............................41
2.4.2 Systems Scientific Classification of Systems .....................................41
2.4.2.1 Natural and Artificial Systems ...........................................41
2.4.2.2 Physical and Abstract (Conceptual) Systems .....................42
2.4.2.3 Static and Dynamic Systems ..............................................42
2.4.2.4 Open and Closed Systems ..................................................43
2.4.3 Classifications of Systems Based on Mathematical Models ..............43
2.5 Systems Defined on Dynamic Sets ..................................................................43
2.5.1 Attributes of Systems .........................................................................44
2.5.2 Subsystems .........................................................................................48
2.5.3 Interactions between Systems ............................................................51
2.5.4 Systems Properties Based on Dynamic Set Theory ...........................51
2.5.4.1 Basic Properties ..................................................................51
2.5.4.2 Systemic Emergence ...........................................................52
2.5.4.3 Stability of Systems ............................................................53
2.5.4.4 Evolution of Systems ..........................................................54
2.5.4.5 Boundary of Systems ..........................................................55
2.6 Open-Ended Problems .....................................................................................56
Chapter 3 Nonlinear Systems Dynamics and Catastrophe .........................................................59
3.1 Mathematical Description of Systems Dynamics ...........................................59
3.1.1 Linear Systems and Nonlinear Systems .............................................59
3.1.2 Kinetic Mechanism of Dynamical Systems .......................................63
3.1.3 Stability and Instability ......................................................................63
3.1.3.1 Stability of Linear System ..................................................68
3.1.3.2 Stability of Nonlinear System.............................................69
3.1.3.3 Lyapunov’s Theorem of Stability (Lyapunov’s
Second Method) ..................................................................69
3.1.4 Fixed Point Stability of 2-D Linear System: A Case Study ...............71
3.2 Dynamic Systems Theory of Nonlinear Systems ...........................................77
3.2.1 Attractor and Purposefulness .............................................................77
3.2.2 Bifurcation ..........................................................................................79
3.2.2.1 Saddle–Node Bifurcation ...................................................81
3.2.2.2 Transcritical Bifurcation .....................................................81
3.2.2.3 Pitchfork Bifurcation ..........................................................81
3.2.2.4 One-Focus-to-Limit-Circle Bifurcation..............................82
3.3 Catastrophe Theory .........................................................................................82
3.3.1 Catastrophe Phenomena and Catastrophe Theory .............................82
3.3.2 Singular Points and Topological Equivalence ....................................83
3.3.3 Thom’s Principle (Potential Function and Subdivision Lemma) .......84
3.3.4 Main Characteristics of Catastrophe ..................................................85
3.3.5 Basic Catastrophe Types ....................................................................86
3.3.6 Typical Applications ...........................................................................87
Contents vii
3.3.6.1 Applications in Economic Systems ....................................88
3.3.6.2 Applications in Military Affairs .........................................89
3.3.6.3 Applications in Social Sciences ..........................................89
3.4 Open-Ended Problems .....................................................................................89
Chapter 4 Self-Organization: Dissipative Structures and Synergetics .......................................91
4.1 Organization and Self-Organization ...............................................................91
4.1.1 General Definitions of Organization and Self-Organization .............91
4.1.2 Definition of Organization and Self-Organization by Set Theory .....92
4.1.3 Some Examples of Self-Organization ................................................94
4.1.3.1 Rayleigh–Bénard Convection .............................................94
4.1.3.2 Belousov–Zhabotinsky Reaction ........................................95
4.1.3.3 Laser ...................................................................................96
4.1.3.4 Continental Drift ................................................................96
4.2 Dissipative Structures ......................................................................................97
4.2.1 Classical and Nonequilibrium Thermodynamics ...............................97
4.2.1.1 Classical Thermodynamics.................................................97
4.2.1.2 Nonequilibrium Thermodynamics .....................................98
4.2.2 Dissipative Structures .......................................................................102
4.2.3 Conditions for Existence of Dissipative System ...............................103
4.2.4 Theoretical Analysis of Dissipative Systems ...................................104
4.3 Synergetics .....................................................................................................107
4.3.1 Basic Concepts .................................................................................107
4.3.2 Order Parameter and Enslaving Principle ........................................108
4.3.3 Hypercycle Theory ...........................................................................110
4.4 Some Philosophical Thoughts .......................................................................111
4.4.1 On Dissipative Structures .................................................................111
4.4.2 On Synergetics .................................................................................113
4.4.2.1 Synergy .............................................................................113
4.4.2.2 Orderliness and Order Parameters ...................................113
4.4.2.3 Slow-Change and Fast-Change Parameters ......................113
4.4.2.4 Analogy: Main Research Method of Synergetics .............113
4.4.3 On Structure, Organization, and Chance .........................................114
4.4.3.1 Structures ..........................................................................114
4.4.3.2 Self-Organization ..............................................................115
4.4.3.3 Chance and Inevitability ...................................................116
4.5 Open-Ended Problems ...................................................................................116
Chapter 5 Chaos ........................................................................................................................117
5.1 Phenomena of Chaos .....................................................................................117
5.2 Definition of Chaos ........................................................................................117
5.2.1 Pseudorandomness ...........................................................................118
5.2.2 Definition of Chaos ..........................................................................119
5.2.3 Period Three Implies Chaos .............................................................120
5.2.3.1 Definition of Periodic Point ..............................................120
5.2.3.2 Sarkovskii Theorem ..........................................................120
5.2.3.3 Li–Yorke Theorem ............................................................121
5.2.4 Characteristics of Chaos ...................................................................121
5.3 Logistic Mapping—Chaos Model .................................................................122
viii Contents
5.3.1 Logistic Mapping .............................................................................122
5.3.2 Feigenbaum’s Constants ...................................................................125
5.4 Phase Space Reconstruction ..........................................................................126
5.5 Lyapunov Exponents .....................................................................................126
5.5.1 The Concept .....................................................................................126
5.5.2 Selection of Parameters ....................................................................128
5.5.3 Method for Small Samples of Data ..................................................129
5.6 Case Studies and Fields of Applications .......................................................132
5.7 Some Philosophical Thoughts on Chaos .......................................................138
5.7.1 Unification of Order and Disorder ...................................................138
5.7.2 Unity of Such Opposites as Determinacy and Randomness ............138
5.7.3 Unification of Universality and Complexity ....................................139
5.7.4 Unification of Driving and Dissipative Forces .................................139
5.8 Chaos of General Single-Relation Systems ...................................................139
5.8.1 Chaos of Single-Relation General Systems ......................................139
5.8.2 Attractors of Single-Relation General Systems ................................142
5.9 Open-Ended Problems ...................................................................................144
Chapter 6 Fractals .....................................................................................................................145
6.1 Different Aspects of Fractals .........................................................................145
6.1.1 Fractal Geometry, Fractal Phenomena, and Multiscale Systems .....145
6.1.2 Topological and Fractal Dimensions and Fractal
Statistical Models ...........................................................................146
6.1.3 Regular Fractals and Similarity Dimensions ...................................149
6.1.4 Irregular Fractals and Correlation Dimensions ...............................154
6.1.4.1 Correlation Dimensionality ..............................................154
6.1.5 Applications of Fractals ...................................................................156
6.1.6 Some Philosophical Thoughts on Fractals .......................................157
6.1.6.1 Universality of Fractal Structures.....................................157
6.1.6.2 Fractal Structures and Self-Organization .........................157
6.1.6.3 Dialectical Relationship between Scales and
Fractal Dimensions ...........................................................158
6.1.6.4 Philosophical Significance of Fractal Theory ..................158
6.2 L-Systems—Analysis and Design .................................................................158
6.2.1 Definition of Simple L-Systems .......................................................159
6.2.1.1 L-Mapping ........................................................................160
6.2.1.2 Simple L-Systems .............................................................161
6.2.2 Properties of Simple L-Systems .......................................................162
6.2.3 Explanation of Holistic Emergence of Systems Using D0L ............165
6.2.4 Design of Simple L-Systems ............................................................167
6.2.4.1 Basic Graph Generation Principle of Simple
L-Systems ...................................................................167
6.2.4.2 Fractal Structure Design Based on D0L ...........................167
6.2.4.3 Fractal Structure Design Based on R0L Systems .............170
6.2.5 Summary ..........................................................................................174
6.3 Iterative Function Systems ............................................................................175
6.3.1 Some Theorems of Iterative Function Systems ................................175
6.3.2 Fractal Images of Iterative Function Systems ..................................178
6.4 Open-Ended Problems ...................................................................................180
Contents ix
Chapter 7 Complex Systems and Complexity ...........................................................................183
7.1 Simple Giant Systems ....................................................................................184
7.1.1 Simple Systems ................................................................................184
7.1.2 Simple Giant Systems .......................................................................187
7.1.3 Traditional Research Method of Simple Giant Systems ..................189
7.2 Characteristic Analysis of Complex Systems ................................................189
7.2.1 Basic Concepts of Complex Systems ...............................................189
7.2.2 Characteristics of Complex Systems ................................................190
7.2.3 Evolution of Complex Systems .........................................................192
7.2.4 Classification of Complex Systems ..................................................193
7.2.5 Research Methods of Complex Systems ..........................................195
7.2.5.1 Combined Qualitative Analysis and Quantitative
Calculation ........................................................................195
7.2.5.2 Combined Microcosmic Analysis and
Macroscopic Synthesis .....................................................195
7.2.5.3 Combined Reductionism and Holism ...............................195
7.2.5.4 Combined Certainty and Uncertainty ..............................196
7.2.5.5 Combined Scientific Reasoning and
Philosophical Thinking ....................................................196
7.2.5.6 Combined Computer Stimulations and Human
Intelligence .......................................................................196
7.3 Complexity ....................................................................................................196
7.3.1 Concept of Complexity .....................................................................196
7.3.2 Classification of Complexities ..........................................................197
7.3.3 Science and Theories of Complexity................................................199
7.4 Cases on Association of Complexity and Simplicity ....................................200
7.4.1 The Phenomena of Three and Complexity .......................................200
7.4.1.1 The Phenomenon of Three in Chinese Idioms .................200
7.4.1.2 The Phenomenon of Three in Fairy Tales and Novels ...........201
7.4.1.3 “Three Begets All Things of the World,” as Claimed
in Tao De Ching ................................................................202
7.4.1.4 Three and Li–Yorke Theorem...........................................202
7.4.1.5 Summary ..........................................................................202
7.4.2 Cellular Automata ............................................................................203
7.4.2.1 The Concept ......................................................................203
7.4.2.2 Classic CA Model .............................................................204
7.4.2.3 Case Demonstrations of CA .............................................206
7.5 Conservation Law of Informational Infrastructure .......................................211
7.5.1 Intuitive Understanding of Systems .................................................211
7.5.2 Physical Essence of Dirac’s Large Number Hypothesis ..................211
7.5.3 Mystery of Solar System’s Angular Momentum ..............................214
7.5.4 Measurement Analysis of Movements of Earth’s Atmosphere ........216
7.5.5 Conservation of Informational Infrastructure ..................................216
7.5.6 Impacts of Conservation Law of Informational Infrastructure ........218
7.6 Open-Ended Problems ...................................................................................219
Chapter 8 Complex Adaptive Systems ......................................................................................221
8.1 Basics of Complex Adaptive Systems ...........................................................221
8.1.1 Santa Fe Institute and Birth of CAS Theory ....................................221