Introduction to the Modeling and Analysis of Complex Systems

I Preliminaries
	Introduction
		Complex Systems in a Nutshell
		Topical Clusters
	Fundamentals of Modeling
		Models in Science and Engineering
		How to Create a Model
		Modeling Complex Systems
		What Are Good Models?
		A Historical Perspective
II Systems with a Small Number of Variables
	Basics of Dynamical Systems
		What Are Dynamical Systems?
		Phase Space
		What Can We Learn?
	Discrete-Time Models I: Modeling
		Discrete-Time Models with Difference Equations
		Classifications of Model Equations
		Simulating Discrete-Time Models with One Variable
		99993em.5Simulating Discrete-Time Models with Multiple Variables
		Building Your Own Model Equation
		99993em.5Building Your Own Model Equations with Multiple Variables
	Discrete-Time Models II: Analysis
		Finding Equilibrium Points
		99993em.5Phase Space Visualization of Continuous-State Discrete-Time Models
		Cobweb Plots for One-Dimensional Iterative Maps
		Graph-Based Phase Space Visualization of Discrete-State Discrete-Time Models
		Variable Rescaling
		99993em.5Asymptotic Behavior of Discrete-Time Linear Dynamical Systems
		Linear Stability Analysis of Discrete-Time Nonlinear Dynamical Systems
	Continuous-Time Models I: Modeling
		Continuous-Time Models with Differential Equations
		Classifications of Model Equations
		Connecting Continuous-Time Models with Discrete-Time Models
		Simulating Continuous-Time Models
		Building Your Own Model Equation
	Continuous-Time Models II: Analysis
		Finding Equilibrium Points
		Phase Space Visualization
		Variable Rescaling
		Asymptotic Behavior of Continuous-Time Linear Dynamical Systems
		Linear Stability Analysis of Nonlinear Dynamical Systems
	Bifurcations
		What Are Bifurcations?
		Bifurcations in 1-D Continuous-Time Models
		Hopf Bifurcations in 2-D Continuous-Time Models
		Bifurcations in Discrete-Time Models
	Chaos
		Chaos in Discrete-Time Models
		Characteristics of Chaos
		Lyapunov Exponent
		Chaos in Continuous-Time Models
III Systems with a Large Number of Variables
	Interactive Simulation of Complex Systems
		Simulation of Systems with a Large Number of Variables
		Interactive Simulation with PyCX
		Interactive Parameter Control in PyCX
		Simulation without PyCX
	Cellular Automata I: Modeling
		Definition of Cellular Automata
		Examples of Simple Binary Cellular Automata Rules
		Simulating Cellular Automata
		Extensions of Cellular Automata
		Examples of Biological Cellular Automata Models
	Cellular Automata II: Analysis
		Sizes of Rule Space and Phase Space
		Phase Space Visualization
		Mean-Field Approximation
		Renormalization Group Analysis to Predict Percolation Thresholds
	Continuous Field Models I: Modeling
		99993em.5Continuous Field Models with Partial Differential Equations
		Fundamentals of Vector Calculus
		99993em.5Visualizing Two-Dimensional Scalar and Vector Fields
		Modeling Spatial Movement
		Simulation of Continuous Field Models
		Reaction-Diffusion Systems
	Continuous Field Models II: Analysis
		Finding Equilibrium States
		Variable Rescaling
		Linear Stability Analysis of Continuous Field Models
		Linear Stability Analysis of Reaction-Diffusion Systems
	Basics of Networks
		Network Models
		Terminologies of Graph Theory
		Constructing Network Models with NetworkX
		Visualizing Networks with NetworkX
		Importing/Exporting Network Data
		Generating Random Graphs
	Dynamical Networks I: Modeling
		Dynamical Network Models
		Simulating Dynamics on Networks
		Simulating Dynamics of Networks
		Simulating Adaptive Networks
	Dynamical Networks II: Analysis of Network Topologies
		Network Size, Density, and Percolation
		Shortest Path Length
		Centralities and Coreness
		Clustering
		Degree Distribution
		Assortativity
		Community Structure and Modularity
	Dynamical Networks III: Analysis of Network Dynamics
		Dynamics of Continuous-State Networks
		Diffusion on Networks
		Synchronizability
		99993em.5Mean-Field Approximation of Discrete-State Networks
		Mean-Field Approximation on Random Networks
		Mean-Field Approximation on Scale-Free Networks
	Agent-Based Models
		What Are Agent-Based Models?
		Building an Agent-Based Model
		Agent-Environment Interaction
		Ecological and Evolutionary Models
	Bibliography
	Index