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) This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. You are free to: Share—copy and redistribute the material in any medium or format Adapt—remix, transform, and build upon the material Thelicensorcannotrevokethesefreedomsaslongasyoufollowthelicenseterms. Under the following terms: Attribution—You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. NonCommercial—You may not use the material for commercial purposes. ShareAlike—If you remix, transform, or build upon the material, you must distribute your contributions under the same license as the original. This publication was made possible by a SUNY Innovative Instruction Technology Grant (IITG). IITG is a competitive grants program open to SUNY faculty and support staff across all disciplines. IITG encourages development of innovations that meet the Power of SUNY’s transformative vision. Published by Open SUNY Textbooks, Milne Library State University of New York at Geneseo Geneseo, NY 14454 iii 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). iv 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, v 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 ix