Bifurcations Part 1, Saddle-Node Bifurcation

Bifurcations are a qualitative change in the dynamics of a system as a parameter is varied, for instance, fixed points disappear and new ones emerge. We focus on the saddle-node bifurcation, the main mechanism for the creation and destruction of new equilibrium points. From 'Nonlinear Dynamics and Chaos' (online course). Next, transcritical bifurcation    • Bifurcations Part 2- Transcritical Bi...  

► CORRECTION at 6:50 Wrong sign under square-root. For x' = r + x^2, the fixed points are at x = +/- sqrt(-r)

► Other bifurcation topics
transcritical bifurcation    • Bifurcations Part 2- Transcritical Bi...  
pitchfork bifurcation    • Bifurcations Part 3- Pitchfork Bifurc...  
robustness of bifurcations    • Bifurcations Part 4- Robustness of Bi...  
bifurcations in 2D systems    • Bifurcations in 2D, Part 1: Introduct...  

► Bifurcations in 2D
Zero eigenvalue bifurcations    • Bifurcations in 2D, Part 1: Introduct...  
Hopf bifurcation theory    • Bifurcations in 2D, Part 2: Hopf Bifu...  
Hopf physical examples    • Bifurcations in 2D, Part 3: Hopf Bifu...  
Bifurcations of limit cycles    • Bifurcations in 2D, Part 4: Global Bi...  

► From 'Nonlinear Dynamics and Chaos'
Online course playlist https://is.gd/NonlinearDynamics

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► Dr. Shane Ross, Virginia Tech professor (Caltech PhD)
http://chaotician.com​

► Course lecture notes (PDF)
https://is.gd/NonlinearDynamicsNotes

► A more in-depth mathematical discussion of bifurcations
   • Bifurcation Theory: Saddle-Node, Hopf...  

Reference: Steven Strogatz, "Nonlinear Dynamics and Chaos", Chapter 3: Bifurcations

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📚Attitude Dynamics and Control
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📚Nonlinear Dynamics and Chaos
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📚Three-Body Problem Orbital Mechanics
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📚Lagrangian and 3D Rigid Body Dynamics
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📚Center Manifolds, Normal Forms, and Bifurcations
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