Resources

Spring 2025 • E91 • Swarthmore College •

Lecture Notes Template

PDF

LaTeX

Numerical Solution of Differential Equations

Tutorial

The Logistic Equation

Interactive Mathematica Notebook

Mathematica *.nb file

Bifurcations

Saddle-Node, Transcritical, and Pitchfork bifurcations

Higher-order Pitchfork Bifurcation

The Phase Plane

pplane Note: You can right-click and save the image generated by pplane.

Mass-spring system

Introduction to Limit Cycles

Forced simple harmonic oscillator and accompanying Mathematica notebook

Bifurcations

Saddle-node, Transcritical, and Pitchfork Bifurcations

Another example of pitchfork bifurcation]

Hopf Bifurcations

Supercritical Hopf

Subcritical Hopf

Higher-order Subcritical Hopf

Infinite-period Hopf

Homoclinic Bifurcation