Introduction to the Modeling and Analysis of Complex Systems

xinterested in complex systems modeling.This OpenSUNY textbook is my humble attempt to meet this need. As someone whodidn’t major in either physics or mathematics, and who moved away from the mainstreamof computer science, I thought I could be a good “translator” of technical material forlaypeople who don’t major in those quantitative fields. To make the material as tangibleas possible, I included a lot of step-by-step instructions on how to develop models (especiallycomputer simulation codes), as well as many visuals, in this book. Those detailedinstructions/visuals may sometimes look a bit redundant, but hopefully they will make thetechnical material more accessible to many of you. I also hope that this book can serveas a good introduction and reference for graduate students and researchers who are newto the field of complex systems.In this textbook, we will use Python for computational modeling and simulation. Pythonis a rapidly growing computer programming language widely used for scientific computingand also for system development in the information technology industries. It is freelyavailable and quite easy to learn for non-computer science majors. I hope that usingPython as a modeling and simulation tool will help you gain some real marketable skills,and it will thus be much more beneficial than using other pre-made modeling/simulationsoftware. All the Python sample codes for modeling examples are available from thetextbook’s website at http://bingweb.binghamton.edu/~sayama/textbook/, which aredirectly linked from each code example shown in this textbook (if you are reading thiselectronically). Solutions for the exercises are also available from this website.To maintain a good balance between accessibility and technical depth/rigor, I havewritten most of the topics in two chapters, one focusing on hands-on modeling work andthe other focusing on more advanced mathematical analysis. Here is a more specificbreakdown:Preliminary chapters 1, 2Modeling chapters 3, 4, 6, 10, 11, 13, 15, 16, 19Analysis chapters 5, 7, 8, 9, 12, 14, 17, 18The preliminary and modeling chapters are marked with an orange side bar at the top,while the analysis chapters are marked with a blue side bar at the bottom. The modelingchapters won’t require any in-depth mathematical skills; some basic knowledge of derivativesand probabilities is enough. The analysis chapters are based on a more solid understandingof calculus, differential equations, linear algebra, and probability and statistics.I hope this unique way of organizing topics in two complementary chapters will provide