Bifurcations in 2D, Part 4 - Global Bifurcations, Limit Cycle Creation - Homoclinic Bifurcation

This lecture examines global bifurcations that create or destroy limit cycles in two-dimensional systems. It compares the amplitude and period scaling of saddle-node, SNIPER, and homoclinic bifurcations, with examples connected to heartbeat and nerve-firing time series.

Syllabus

Introduction.
saddle-node bifurcation of cycles, or fold bifurcation.
saddle-node infinite-period bifurcation on a cycle, or SNIPER.
connection with heartbeat or nerve firing time-series.
homoclinic bifurcation, or saddle-loop .
universal behavior of bifurcations of cycles, a summary of the amplitude and period of the resulting limit cycles as a function of the distance of the parameter from the critical value.