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 Bifurcatio...
- Transcritical bifurcations • Transcritical Bifurcat...
- Pitchfork bifurcations • Pitchfork Bifurcations...
Lecture series on dynamical systems: • Welcome - Dynamical Sy...
Lectures series on differential equations: • Welcome - Ordinary Dif...
More information on the instructor: hybrid.concord...
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[@LouisGariepy]

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[@nicklamonica8647]

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[@jasonbramburger]

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[@nicklamonica8647]

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