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

Explore global bifurcations and limit cycle creation in two-dimensional systems through this comprehensive video lecture. Delve into four common ways limit cycles are created or destroyed, focusing on global bifurcations that involve large regions of the phase plane. Learn about saddle-node bifurcation of cycles, saddle-node infinite-period bifurcation on a cycle (SNIPER), and homoclinic bifurcation. Discover the connection between these concepts and real-world applications like heartbeat and nerve firing time-series. Gain insights into the universal behavior of bifurcations of cycles, including the amplitude and period of resulting limit cycles as a function of parameter distance from critical values. This in-depth exploration builds on previous knowledge of local bifurcations and provides a foundation for understanding more complex dynamical systems.

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.