Bifurcations of Limit Cycles - Dynamical Systems Extra Credit | Lecture 7 скачать в хорошем качестве

Bifurcations of Limit Cycles - Dynamical Systems Extra Credit | Lecture 7

Just like fixed points, limit cycles can undergo bifurcations as well. In this lecture we review three of the main limit cycle bifurcations. We will see that limit cycles can emerge through saddle-node bifurcations, while also showing that saddle-node bifurcations of fixed points can occur on the limit cycle itself. We also examine a global bifurcation - the homoclinic bifurcation - where a limit cycle expands until it attaches itself to a fixed point and creates a homoclinic orbit. Example systems exhibiting each type of bifurcation are provided throughout this lecture. Recall bifurcations of fixed points with these lectures: Saddle-node bifurcations    • Saddle Node Bifurcations - Dynamical Syste...   Transcritical bifurcations    • Transcritical Bifurcations - Dynamical Sys...   Pitchfork bifurcations    • Pitchfork Bifurcations - Dynamical Systems...   Lecture series on dynamical systems:    • Welcome - Dynamical Systems | Intro Lecture   Lectures series on differential equations:    • Welcome - Ordinary Differential Equations ...   More information on the instructor: https://hybrid.concordia.ca/jbrambur/ Follow @jbramburger7 on Twitter for updates.