Explore a novel algorithm for decomposing chaos into a linear system with intermittent forcing in this comprehensive video lecture. Delve into the Hankel Alternative View of Koopman (HAVOK) analysis, which constructs linear regression models on eigen-time-delay coordinates. Learn about dynamical systems, sensitivity to initial conditions, and Koopman operator theory. Discover how HAVOK analysis applies embedding theorems and builds regression models to analyze chaotic systems. Examine the results, including prediction capabilities and nonlinearity modeling. Access the provided MATLAB code to implement the HAVOK analysis on the Lorenz model. Gain insights into this groundbreaking approach to understanding and modeling chaotic systems through detailed explanations and practical demonstrations.
Overview
Syllabus
Introduction
Dynamical Systems
Sensitivity to Initial Conditions
Koopman Operator Theory
Invariant Subspaces
HAVOK Analysis
Embedding Theorem
Koopman in Habit
Building a Regression Model
Results
Prediction
Nonlinearity
Model
Download
MATLAB Model
Lorenz Model
Conclusion
Taught by
Steve Brunton
