Introduction to the Modeling and Analysis of Complex Systems

498 Pages·2015·18.71 MB·English

Introduction to the Modeling and Analysis of
Complex Systems
Hiroki Sayama
(cid:13)c2015 Hiroki Sayama
ISBN:
978-1-942341-06-2 (deluxe color edition)
978-1-942341-08-6 (print edition)
978-1-942341-09-3 (ebook)
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Published by Open SUNY Textbooks, Milne Library
State University of New York at Geneseo
Geneseo, NY 14454
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About the Textbook
Introduction to the Modeling and Analysis of Complex Systems introduces students to
mathematical/computational modeling and analysis developed in the emerging interdis-
ciplinary field of Complex Systems Science. Complex systems are systems made of a
large number of microscopic components interacting with each other in nontrivial ways.
Many real-world systems can be understood as complex systems, where critically impor-
tant information resides in the relationships between the parts and not necessarily within
the parts themselves.
Thistextbookoffersanaccessibleyettechnically-orientedintroductiontothemodeling
and analysis of complex systems. The topics covered include: fundamentals of modeling,
basicsofdynamicalsystems,discrete-timemodels,continuous-timemodels,bifurcations,
chaos,cellularautomata,continuousfieldmodels,staticnetworks,dynamicnetworks,and
agent-basedmodels. Mostofthesetopicsarediscussedintwochapters,onefocusingon
computational modeling and the other on mathematical analysis. This unique approach
provides a comprehensive view of related concepts and techniques, and allows readers
and instructors to flexibly choose relevant materials based on their objectives and needs.
Python sample codes are provided for each modeling example.
About the Author
Hiroki Sayama, D.Sc., is an Associate Professor in the Department of Systems Science
and Industrial Engineering, and the Director of the Center for Collective Dynamics of
Complex Systems (CoCo), at Binghamton University, State University of New York. He
received his BSc, MSc and DSc in Information Science, all from the University of Tokyo,
Japan. He did his postdoctoral work at the New England Complex Systems Institute in
Cambridge, Massachusetts, from 1999 to 2002. His research interests include complex
dynamicalnetworks, humanandsocialdynamics,collectivebehaviors,artificiallife/chem-
istry, and interactive systems, among others.
He is an expert of mathematical/computational modeling and analysis of various com-
plex systems. He has published more than 100 peer-reviewed journal articles and confer-
ence proceedings papers and has edited eight books and conference proceedings about
complex systems related topics. His publications have acquired more than 2000 citations
as of July 2015. He currently serves as an elected Board Member of the International
Society for Artificial Life (ISAL) and as an editorial board member for Complex Adaptive
Systems Modeling (SpringerOpen), International Journal of Parallel, Emergent and Dis-
tributed Systems (Taylor & Francis), and Applied Network Science (SpringerOpen).
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Reviewer’s Notes
This book provides an excellent introduction to the field of modeling and analysis of com-
plexsystemstobothundergraduateandgraduatestudentsinthephysicalsciences,social
sciences, health sciences, humanities, and engineering. Knowledge of basic mathemat-
icsispresumedofthereaderwhoisgivenglimpsesintothevast,diverseandrichworldof
nonlinear algebraic and differential equations that model various real-world phenomena.
The treatment of the field is thorough and comprehensive, and the book is written in a
very lucid and student-oriented fashion. A distinguishing feature of the book, which uses
the freely available software Python, is numerous examples and hands-on exercises on
complex system modeling, with the student being encouraged to develop and test his or
her own code in order to gain vital experience.
The book is divided into three parts. Part I provides a basic introduction to the art
and science of model building and gives a brief historical overview of complex system
modeling. Part II is concerned with systems having a small number of variables. After
introducing the reader to the important concept of phase space of a dynamical system,
it covers the modeling and analysis of both discrete- and continuous-time systems in a
systematic fashion. A very interesting feature of this part is the analysis of the behavior of
such a system around its equilibrium state, small perturbations around which can lead to
bifurcations and chaos. Part III covers the simulation of systems with a large number of
variables. After introducing the reader to the interactive simulation tool PyCX, it presents
the modeling and analysis of complex systems (e.g., waves in excitable media, spread
of epidemics and forest fires) with cellular automata. It next discusses the modeling and
analysis of continuous fields that are represented by partial differential equations. Exam-
ples are diffusion-reaction systems which can exhibit spontaneous self-organizing behav-
ior (e.g., Turing pattern formation, Belousov-Zhabotinsky reaction and Gray-Scott pattern
formation). Part III concludes with the modeling and analysis of dynamical networks and
agent-based models.
Theconceptsofemergenceandself-organizationconstitutetheunderlyingthreadthat
weaves the various chapters of the book together.
About the Reviewer: Dr. Siddharth G. Chatterjee received his Bachelor’s Degree in Tech-
nology (Honors) from the Indian Institute of Technology, Kharagpur, India, and M.S. and
Ph.D. degrees from Rensselaer Polytechnic Institute, Troy, New York, USA, all in Chem-
ical Engineering. He has taught a variety of engineering and mathematical courses and
his research interests are the areas of philosophy of science, mathematical modeling and
simulation. Presently he is Associate Professor in the Department of Paper and Biopro-
cess Engineering at SUNY College of Environmental Science and Forestry, Syracuse,
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New York. He is also a Fellow of the Institution of Engineers (India) and Member of the
Indian Institute of Chemical Engineers.
Sayama has produced a very comprehensive introduction and overview of complexity.
Typically, these topics would occur in many different courses, as a side note or possible
behavior of a particular type of mathematical model, but only after overcoming a huge
hurdle of technical detail. Thus, initially, I saw this book as a “mile-wide, inch-deep” ap-
proach to teaching dynamical systems, cellular automata, networks, and the like. Then
I realized that while students will learn a great deal about these topics, the real focus is
learning about complexity and its hallmarks through particular mathematical models in
which it occurs. In that respect, the book is remarkably deep and excellent at illustrating
how complexity occurs in so many different contexts that it is worth studying in its own
right. In other words, Sayama sort of rotates the axes from “calculus”, “linear algebra”,
and so forth, so that the axes are “self-organization”, “emergence”, etc. This means that I
would be equally happy to use the modeling chapters in a 100-level introduction to mod-
eling course or to use the analysis chapters in an upper-level, calculus-based modeling
course. The Python programming used throughout provides a nice introduction to simula-
tion and gives readers an excellent sandbox in which to explore the topic. The exercises
provide an excellent starting point to help readers ask and answer interesting questions
about the models and about the underlying situations being modeled. The logical struc-
ture of the material takes maximum advantage of early material to support analysis and
understanding of more difficult models. The organization also means that students expe-
riencing such material early in their academic careers will naturally have a framework for
later studies that delve more deeply into the analysis and application of particular mathe-
matical tools, like PDEs or networks.
AbouttheReviewer: Dr.KrisGreenearnedhisPh.D.inappliedmathematicsfromtheUni-
versity of Arizona. Since then, he has earned the rank of full professor at St. John Fisher
College where he often teaches differential equations, mathematical modeling, multivari-
ablecalculusandnumericalanalysis,aswellasavarietyofothercourses. Hehasguided
a number of successful undergraduate research projects related to modeling of complex
systems, and is currently interested in applications of such models to education, both in
terms of teaching and learning and of the educational system as a whole. Outside of the
office, he can often be found training in various martial arts or enjoying life with his wife
and two cats.

To Mari

Preface
Thisisanintroductorytextbookabouttheconceptsandtechniquesofmathematical/com-
putational modeling and analysis developed in the emerging interdisciplinary field of com-
plex systems science. Complex systems can be informally defined as networks of many
interacting components that may arise and evolve through self-organization. Many real-
world systems can be modeled and understood as complex systems, such as political
organizations, human cultures/languages, national and international economies, stock
markets, the Internet, social networks, the global climate, food webs, brains, physiolog-
ical systems, and even gene regulatory networks within a single cell; essentially, they
are everywhere. In all of these systems, a massive amount of microscopic components
are interacting with each other in nontrivial ways, where important information resides in
the relationships between the parts and not necessarily within the parts themselves. It
is therefore imperative to model and analyze how such interactions form and operate in
order to understand what will emerge at a macroscopic scale in the system.
Complex systems science has gained an increasing amount of attention from both in-
side and outside of academia over the last few decades. There are many excellent books
alreadypublished,whichcanintroduceyoutothebigideasandkeytake-homemessages
about complex systems. In the meantime, one persistent challenge I have been having in
teaching complex systems over the last several years is the apparent lack of accessible,
easy-to-follow, introductory-level technical textbooks. What I mean by technical textbooks
are the ones that get down to the “wet and dirty” details of how to build mathematical or
computational models of complex systems and how to simulate and analyze them. Other
books that go into such levels of detail are typically written for advanced students who are
alreadydoingsome kindofresearchin physics, mathematics, orcomputer science. What
I needed, instead, was a technical textbook that would be more appropriate for a broader
audience—college freshmen and sophomores in any science, technology, engineering,
and mathematics (STEM) areas, undergraduate/graduate students in other majors, such
asthesocialsciences,management/organizationalsciences,healthsciencesandthehu-
manities, and even advanced high school students looking for research projects who are
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