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## Program
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This course has **10 live in-person sessions**.
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This site is organized around **eight core modules** plus one extra Lorenz attractor module.
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### 1D ODEs (SciPy + Streamlit)
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The sidebar navigation is the ground-truth order for the material, and this page follows the same structure.
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Simulate classical one-dimensional ODE models (SIR epidemiological model, spruce budworm population model, Michaelis–Menten enzyme kinetics). Solve ODEs numerically with SciPy in Python, and build/deploy a simple Streamlit web app to explore parameter effects. Groups are assigned and remain for the whole course.
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### ODEs in 1D
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### 2D ODEs (Nonlinear Oscillators)
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Build the first simulation workflow with one-dimensional ODEs. You solve IVPs with `scipy.integrate.solve_ivp`, compare trajectories, and interpret parameter changes through the SIR epidemic model, Michaelis-Menten kinetics, and the spruce budworm model.
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Explore two-dimensional ODEs via nonlinear oscillatory systems: Van der Pol oscillator and FitzHugh–Nagumo model. Create animations with matplotlib and build interactive Python programs that let users set initial conditions via mouse clicks.
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### ODEs in 2D
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### Coupled ODEs (Kuramoto Model)
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Move from scalar models to planar dynamics. You work with the CDIMA reaction, the Van der Pol oscillator, and the FitzHugh-Nagumo model, then animate trajectories and phase portraits to study oscillations and excitability.
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Implement coupled ODEs, focusing on the Kuramoto model. Animate multiple plots simultaneously (e.g., oscillator evolution and a bifurcation diagram).
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### Coupled ODEs
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### Collective Motion (Vicsek Model)
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Study synchronization through the Kuramoto model. You simulate many interacting oscillators, track order parameters, and connect time-domain behavior with summary diagrams.
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Simulate flocking behavior using the Vicsek model. Implement interaction rules for “boids” and extend the simulation by treating the mouse as a predator and coding avoidance behavior.
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### Collective Motion
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### Networks I (NetworkX Fundamentals)
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Model flocking and alignment in continuous space. The main case studies use Vicsek and Couzin-style rules, then extend them with interactive animation and predator avoidance.
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Introduce NetworkX: build graphs, compute structural metrics (degree distribution, clustering coefficient, centrality), and visualize different network types. Establish foundations for modeling dynamics on networks.
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### Networks
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### PDEs via Reaction-Diffusion Systems
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Represent systems as graphs with `networkx`. You measure connectivity and centrality, generate standard graph models, and simulate SIS and SIR spreading on synthetic and real networks.
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Introduce partial differential equations through reaction-diffusion models (Gierer-Meinhardt and Gray-Scott). Implement 1D and 2D Laplacians with NumPy and animate spatiotemporal evolution to study Turing instability and pattern formation.
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### Partial Differential Equations
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### Networks II (Spreading on Real Networks)
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Discretize reaction-diffusion systems in one and two spatial dimensions. You build Laplacians with finite differences, study Turing instability, and simulate Gierer-Meinhardt and Gray-Scott pattern formation.
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Simulate spreading processes (fake news, epidemics) on real-world networks. Retrieve and process open-source network datasets, and investigate how network structure shapes propagation dynamics.
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### Cellular Automata
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### Cellular Automata I (1D CA)
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Switch from continuous fields to fully discrete local rules. You implement one-dimensional cellular automata, build space-time diagrams, and compare how rule choice and initial conditions affect long-run behavior.
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Introduce one-dimensional cellular automata as a framework for discrete dynamical systems. Explore deterministic and stochastic CA, and how simple local rules generate complex global behavior.
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### Agent-Based Modeling
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### Cellular Automata II (Traffic Dynamics)
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Use traffic as the main agent-based case study. You implement the Nagel-Schreckenberg model, visualize stop-and-go waves, and measure density, flow, and congestion.
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Apply cellular automata to traffic modeling with the Nagel–Schreckenberg model. Study congestion, flow, and phase transitions by tuning parameters such as vehicle density and maximum speed.
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### Extra: Lorenz Attractor
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### Final Project Support
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Wrap-up and support session for the final project: address remaining questions, clarify concepts, and help groups prepare deliverables.
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Extend the ODE material into deterministic chaos. You simulate the Lorenz system, plot the attractor in three dimensions, and measure sensitivity to initial conditions.
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