Week 2: CX-202 Complex Systems Modeling and Networks
Additional Note (6/25/2008): Asterisks show your responses to yesterday's survey. It seems there are needs for non-spatial models, agent-based models and network models. So I will try to spend more time on these topics. Hopefully we will be able to touch some of the ABM stuff today.
About Modeling Tools
We plan to use Microsoft Excel as a simple modeling platform for the first two modules. You may use other spreadsheet software that has capabilities similar to Excel.
For the last three lab modules, we will use Python as a primary programming language. Download and install the following to your laptop:
Here are some useful links:
Wed June 25
- 9:00am-10:30am Fundamentals of Modeling [slides]
- Introduction
- Modeling in Science and Engineering
- How to Create a Model? **
- How to Evaluate a Model? *
- 10:40am-12:10pm Non-Spatial Models [slides] [timeseries.py] [logisticmap.py] [popsongmodel.py] ***
- Discrete-Time Models
- Developing Discrete-Time Models with One Variable
- Logistic Map and Chaos **
- Developing Discrete-Time Models with Multiple Variables
- Continuous-Time Models
- Modeling Exercises
- 1:00pm-2:30pm Cellular Automata [slides] [1Ddiffusion.py] [droplet.py] [GoL.py]
- 2:40pm-4:10pm Cellular Automata: Lab
- Spatio-Temporal Dynamics on Locally Connected Networks **
- Cellular Automata: A Simplified Discrete-State Model*
- Modeling Exercises
- 4:20pm-5:00pm Q&As and Discussions
Thu June 26
Week 3: CX-203 Methods for the Study of Complex Systems
Mon June 30
- Introduction / Iterative Maps [slides]
[cobwebplot.py] [bifurcationdiagram.py] [lyapunovexponent.py]
- Review of Difference Equations
- Iterative Maps
- Logistic Map and Chaos
- Characteristics of Chaos
- Stochastic Systems [slides]
- Random Walk
- Self-Similar Properties of Individual Random Walk
- Transition Probability Matrix and Asymptotic Probability Distribution
- An Application: Google's "PageRank"
- Information Theory [slides]
- Quantitative Definition of Information
- Information Entropy
- Information Entropy and Multiple Probability Spaces
- Mutual Information
- Information Source
- Calculating Entropy of Markov Information Source
Tue July 1
- Dynamical Systems and Phase Space [slides]
[phaseportrait.py]
- Geometrical Approach to Dynamical Systems
- Visualizing Phase Space of Discrete Models
- Visualizing Phase Space of Continuous Models
- Linear Systems
- Asymptotic Behavior of Linear Systems
- Nonlinear Systems
- Analytical Tools for Dynamical Systems [slides]
- Local Linearization and Linear Stability Analysis
- Bifurcations
- Bifurcations in 1-D Systems
- Limit Cycles and Hopf Bifurcations in Higher-Dimensional Systems
- Hopf Bifurcations in Neuronal Models
- Chaos in Continuous-Time Models
- Mean-Field Approximation
- Partial Differential Equations and Reaction-Diffusion Systems [slides]
- Continuous Field Models
- Developing PDE-Based Models
- Analytical Treatments of Spatially Distributed Systems
- Reaction-Diffusion Equations
- Computation Theory [slides]
- Propositional Logic
- Proof and Inference
- Automata and Formal Languages
- Turing Machines
- Computational Universality and Universal Turing Machines
- The Halting Problem
- Cellular Automata [slides]
- Review of Cellular Automata
- Phase Space of Cellular Automata
- Converting PDE Models into CA with Real-Valued States
- Other Extensions of Cellular Automata
Wed July 2 & Thu July 3: Taught by Prof. Yaneer Bar-Yam and Prof. Irv Epstein
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