Free

Sayama

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

By Unknown

Free

Read Now

The publisher has enabled DRM protection, which means that you need to use the BookFusion iOS, Android or Web app to read this eBook. This eBook cannot be used outside of the BookFusion platform.

Description Table of Contents Reviews

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