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Sayama

Name: Sayama
ISBN: 978-1-942341-06-2

By Unknown

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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
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