Introduction to the Modeling and Analysis of Complex Systems
Author(s):
Hiroki Sayama
Publication Date: August 13, 2015
ISBN: 9781942341062
OCLC: 918567125
Affiliation: SUNY Binghamton
About the book
Keep up to date on Introduction to Modeling and Analysis of Complex Systems at http://bingweb.binghamton.edu/~sayama/textbook/!
Introduction to the Modeling and Analysis of Complex Systems introduces students to mathematical/computational modeling and analysis developed in the emerging interdisciplinary 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 important information resides in the relationships between the parts and not necessarily within the parts themselves. This textbook offers an accessible yet technically-oriented introduction to the modeling and analysis of complex systems. The topics covered include: fundamentals of modeling, basics of dynamical systems, discrete-time models, continuous-time models, bifurcations, chaos, cellular automata, continuous field models, static networks, dynamic networks, and agent-based models. Most of these topics are discussed in two chapters, one focusing on 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.
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REVIEWS:
Hiroki Sayama’s book “Introduction to the Modeling and Simulation of Complex Systems” is … a unique and welcome addition to any instructor’s collection. What makes it valuable is that it not only presents a state-of-the-art review of the domain but also serves as a gentle guide to learning the sophisticated art of modeling complex systems.
–Muaz A. Niazi, Complex Adaptive Systems Modeling 2016 4:3
… Sayamaʼs book is a very good instrument for students who want to read an introductory text on modeling and analysis of complex systems, and for instructors who need such a text in simple language for their complex systems courses and projects. The book offers a good introduction to the complex systems terminology and plenty of readily available examples with technical implementation details. … Overall, Introduction to the Modeling and Analysis of Complex Systems offers a novel pedagogical approach to the teaching of complex systems, based on examples and library code that engage students in a tutorial-style learning adventure. It is a solid tool that may become one of the primary instruments for teaching complex systems science and help the discipline to become more established in the academic world, triggering the necessary transition from a top-down tradition to a bottom-up complex systems approach.
-Stefano Nichele, Artificial Life 22(3): 424-427, 2016. www.mitpressjournals.org/doi/abs/10.1162/ARTL_r_00209
Table of Contents
- I Preliminaries
- 1 Introduction
- 1.1 Complex Systems in a Nutshell
- 1.2 Topical Clusters
- 2 Fundamentals of Modeling
- 2.1 Models in Science and Engineering
- 2.2 How to Create a Model
- 2.3 Modeling Complex Systems
- 2.4 What Are Good Models?
- 2.5 A Historical Perspective
- II Systems with a Small Number of Variables
- 3 Basics of Dynamical Systems
- 3.1 What Are Dynamical Systems?
- 3.2 Phase Space
- 3.3 What Can We Learn?
- 4 Discrete-Time Models I: Modeling
- 4.1 Discrete-Time Models with Difference Equations
- 4.2 Classifications of Model Equations
- 4.3 Simulating Discrete-Time Models with One Variable
- 4.4 Simulating Discrete-Time Models with Multiple Variables
- 4.5 Building Your Own Model Equation
- 4.6 Building Your Own Model Equations with Multiple Variables
- 5 Discrete-Time Models II: Analysis
- 5.1 Finding Equilibrium Points
- 5.2 Phase Space Visualization of Continuous-State Discrete-Time Models
- 5.3 Cobweb Plots for One-Dimensional Iterative Maps
- 5.4 Graph-Based Phase Space Visualization of Discrete-State Discrete-Time Models
- 5.5 Variable Rescaling
- 5.6 Asymptotic Behavior of Discrete-Time Linear Dynamical Systems
- 5.7 Linear Stability Analysis of Discrete-Time Nonlinear Dynamical Systems
- 6 Continuous-Time Models I: Modeling
- 6.1 Continuous-Time Models with Differential Equations
- 6.2 Classifications of Model Equations
- 6.3 Connecting Continuous-Time Models with Discrete-Time Models
- 6.4 Simulating Continuous-Time Models
- 6.5 Building Your Own Model Equation
- 7 Continuous-Time Models II: Analysis
- 7.1 Finding Equilibrium Points
- 7.2 Phase Space Visualization
- 7.3 Variable Rescaling
- 7.4 Asymptotic Behavior of Continuous-Time Linear Dynamical Systems
- 7.5 Linear Stability Analysis of Nonlinear Dynamical Systems
- 8 Bifurcations
- 8.1 What Are Bifurcations?
- 8.2 Bifurcations in 1-D Continuous-Time Models
- 8.3 Hopf Bifurcations in 2-D Continuous-Time Models
- 8.4 Bifurcations in Discrete-Time Models
- 9 Chaos
- 9.1 Chaos in Discrete-Time Models
- 9.2 Characteristics of Chaos
- 9.3 Lyapunov Exponent
- 9.4 Chaos in Continuous-Time Models
- III Systems with a Large Number of Variables
- 10 Interactive Simulation of Complex Systems
- 10.1 Simulation of Systems with a Large Number of Variables
- 10.2 Interactive Simulation with PyCX
- 10.3 Interactive Parameter Control in PyCX
- 10.4 Simulation without PyCX
- 11 Cellular Automata I: Modeling
- 11.1 Definition of Cellular Automata
- 11.2 Examples of Simple Binary Cellular Automata Rules
- 11.3 Simulating Cellular Automata
- 11.4 Extensions of Cellular Automata
- 11.5 Examples of Biological Cellular Automata Models
- 12 Cellular Automata II: Analysis
- 12.1 Sizes of Rule Space and Phase Space
- 12.2 Phase Space Visualization
- 12.3 Mean-Field Approximation
- 12.4 Renormalization Group Analysis to Predict Percolation Thresholds
- 13 Continuous Field Models I: Modeling
- 13.1 Continuous Field Models with Partial Differential Equations
- 13.2 Fundamentals of Vector Calculus
- 13.3 Visualizing Two-Dimensional Scalar and Vector Fields
- 13.4 Modeling Spatial Movement
- 13.5 Simulation of Continuous Field Models
- 13.6 Reaction-Diffusion Systems
- 14 Continuous Field Models II: Analysis
- 14.1 Finding Equilibrium States
- 14.2 Variable Rescaling
- 14.3 Linear Stability Analysis of Continuous Field Models
- 14.4 Linear Stability Analysis of Reaction-Diffusion Systems
- 15 Basics of Networks
- 15.1 Network Models
- 15.2 Terminologies of Graph Theory
- 15.3 Constructing Network Models with NetworkX
- 15.4 Visualizing Networks with NetworkX
- 15.5 Importing/Exporting Network Data
- 15.6 Generating Random Graphs
- 16 Dynamical Networks I: Modeling
- 16.1 Dynamical Network Models
- 16.2 Simulating Dynamics on Networks
- 16.3 Simulating Dynamics of Networks
- 16.4 Simulating Adaptive Networks
- 17 Dynamical Networks II: Analysis of Network Topologies
- 17.1 Network Size, Density, and Percolation
- 17.2 Shortest Path Length
- 17.3 Centralities and Coreness
- 17.4 Clustering
- 17.5 Degree Distribution
- 17.6 Assortativity
- 17.7 Community Structure and Modularity
- 18 Dynamical Networks III: Analysis of Network Dynamics
- 18.1 Dynamics of Continuous-State Networks
- 18.2 Diffusion on Networks
- 18.3 Synchronizability
- 18.4 Mean-Field Approximation of Discrete-State Networks
- 18.5 Mean-Field Approximation on Random Networks
- 18.6 Mean-Field Approximation on Scale-Free Networks
- 19 Agent-Based Models
- 19.1 What Are Agent-Based Models?
- 19.2 Building an Agent-Based Model
- 19.3 Agent-Environment Interaction
- 19.4 Ecological and Evolutionary Models
- Bibliography
- Index
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 dynamical networks, human and social dynamics, collective behaviors, artificial life/chemistry, and interactive systems, among others. He is an expert of mathematical/computational modeling and analysis of various complex systems. He has published more than 100 peer-reviewed journal articles and conference 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 Distributed Systems (Taylor & Francis), and Applied Network Science (SpringerOpen).
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