Relaxation Oscillator

April 20, 2017 Leave a comment

Professor Strogatz Cornell course video lectures on “Nonlinear Dynamics and Chaos” are now online. This post pays homage to lecture 10 on analysis of the  Van der Pol equaltion:

\ddot{x}+x+\mu \dot{x}(x^2-1)=0

In the following the case for \mu =2,\mu =10 and the examination of the \mu >>1. It nicely illustrates the two time scales referred to, the slow then fast parts of the oscillation.

The phase portrait is the x, y plane where y is the the Lienard transformed and rescaled version of the equation.

So the system is:



Categories: Uncategorized


April 4, 2017 Leave a comment


Categories: Uncategorized

Double Pendulum

March 31, 2017 Leave a comment


Categories: Uncategorized

Chronic Mitral Regurgitation Misconception

March 29, 2017 Leave a comment

Gaasch et al report an interesting study looking at the commonly expressed “low impedance” retrograde regurgitant volume. This graphic uses the mathematical model in the paper:


Categories: Uncategorized

Pi By Any Other Name

March 23, 2017 Leave a comment

coprimepiThis post is motivated by this video by standupmath (Matt Parker).

This simulates the procedure in the video (different upper bounds of integers and sample sizes):

Categories: Uncategorized

Ask a Dead Salmon

March 6, 2017 Leave a comment

I found this on “Calling Bullshit”. It is no doubt a wonderful illustration of spurious correlation. It made me laugh out loud.



Categories: Uncategorized

More Hypocycloid Fun

February 27, 2017 Leave a comment

The generalization of hypocycloid in hypocycloid. In this case 5,11:



Categories: Uncategorized