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By the end of this section, you should
Understand how non-linear systems may behave much differently than linear systems
Trajectories can vary wildly due to small changes in initial values or parameters
Understand what phase plane is and how it is created
Understand what is meant by chaos and how it differs from “randomness”
Introduction
Introduction
Lorenz System
Lorenz System
Supplemental Lorenz Information
Supplemental Lorenz Information
https://www.technologyreview.com/s/422809/when-the-butterfly-effect-took-flight/
Varying Initial Conditions
Varying Initial Conditions
Varying System Parameters
Varying System Parameters
Monte Carlo Simulation
Monte Carlo Simulation
https://www.ecmwf.int/en/about/media-centre/fact-sheet-ensemble-weather-forecasting
A Clockwork Universe?
A Clockwork Universe?
Why Should We Care?
Why Should We Care?
Mappings
Mappings
Logistic Map
Logistic Map
Bifurcation
Bifurcation
Stability
Stability
Limit Cycles
Limit Cycles
Phase Portraits
Phase Portraits
Lecture Code
Lecture Code
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