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Book Description

Table of Contents

- 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

- Introduction
- 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

- Basics of Dynamical Systems
- 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

- Interactive Simulation of Complex Systems

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