Continuous_time.gif

Discrete_time.gif

Discrete_time_2.gif

LS 30B intro lecture - brief review of LS 30A.ipynb

Mini-Lecture 1 - Periodic functions.ipynb

Mini-Lecture 12 - Behavior of the CO2 ventilation (Mackeyâ€“Glass) model.ipynb

Mini-Lecture 14 - Negative feedback and time delay.ipynb

Mini-Lecture 15 - The Hopf bifurcation diagram.ipynb

Mini-Lecture 2 - Attractors, and limit cycle attractors.ipynb

Mini-Lecture 5 - The HPG model.ipynb

Mini-Lecture 5-04 - The defining properties of chaos.ipynb

Mini-Lecture 5-05 - More about sensitive dependence on initial conditions.ipynb

Mini-Lecture 5-06 - The attractor in a chaotic model.ipynb

Mini-Lecture 5-07 - Patterns in chaos.ipynb

Mini-Lecture 5-09 - The chaotic attractor of a 1-variable discrete-time model.ipynb

Mini-Lecture 5-1 - From 2D dynamics to 3D dynamics.ipynb

Mini-Lecture 5-10 - Bifurcations in the discrete-time logistic model.ipynb

Mini-Lecture 5-2 - Discrete-time models of dynamical systems.ipynb

Mini-Lecture 5-3 - Exponential growth in continuous time and discrete time.ipynb

Mini-Lecture 6 - Behavior of the HPG model.ipynb

Mini-Lecture 6-17 - Eigenvalues and eigenvectors.ipynb

Mini-Lecture 6-23 - Exponential growth or decay in multiple dimensions.ipynb

Mini-Lecture 6-30 - Complex eigenvalues.ipynb

Mini-Lecture 6-31 - Linear differential equations (continuous time) - The diagonal case.ipynb

Mini-Lecture 6-32 - A model of the loggerhead sea turtle population.ipynb

Mini-Lecture 6-32 - Linear differential equations (continuous time) - The general case.ipynb

Mini-Lecture 6-35 - Linear dynamics in 3D.ipynb

Mini-Lecture 7 - How a limit cycle attractor forms.ipynb

Mini-Lecture 7-03 - The graph of a function f(X,Y).ipynb

Mini-Lecture 7-04 - Linear approximation of a function f(X,Y).ipynb

Mini-Lecture 7-07 - Examples of classifying equilibrium points (linear approximation of a vector field).ipynb

Mini-Lecture 7-08 - The tangent plane of a function.ipynb

Mini-Lecture 7-09 - How a Hopf bifurcation occurs, part 2.ipynb

Mini-Lecture 7-10 - Hopf bifurcation in the HPG model.ipynb

Mini-Lecture 7-11 - The Hartmanâ€“Grobman Theorem, and where linear stability analysis fails.ipynb

Mini-Lecture 8 - How a Hopf bifurcation occurs.ipynb

Mini-Lecture 9 - Saturating functions, sigmoid functions, etc.ipynb

Mini-lecture 7-12 - Intro to optimization.ipynb

Mini-lecture 7-16 - Critical points of functions of multiple variables.ipynb

Mini-lecture 7-17 - The gradient vector field of a function of multiple variables.ipynb

Sharks and Tuna 1.gif

Sharks and Tuna 2.gif

images/