Sayama
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Description
Contents
Reviews
Language
Unknown
ISBN
978-1-942341-06-2
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
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