Class Central is learner-supported. When you buy through links on our site, we may earn an affiliate commission.

YouTube

Bifurcation Theory - Saddle-Node, Hopf, Transcritical, Pitchfork

Ross Dynamics Lab via YouTube

Start learning Write review
Scrimba Ad

Get 20% off all career paths from fullstack to AI

Learn More → Coursera Ad

AI, Data Science & Cloud Certificates from Google, IBM & Meta

Learn More →

Overview

Google, IBM & Meta Certificates – 40% Off
One Coursera Plus subscription covers most Professional Certificates on Coursera.
Unlock All Certificates
This lecture develops local bifurcation theory near fixed points of vector fields and maps. It uses one-dimensional center-manifold dynamics to analyze saddle-node, transcritical, pitchfork, period-doubling, and Hopf bifurcations.

Syllabus

Local Bifurcation Theory.
System in n dimensions, only look at center manifold directions.
saddle-node bifurcation,.
transcritical bifurcation,.
pitchfork bifurcation,.
period-doubling bifurcation for maps, related to the period doubling cascade (it's like a pitchfork bifurcation for maps).
Hopf bifurcation for vector fields and maps, the generation of periodic orbits out of fixed points.

Taught by

Ross Dynamics Lab

Reviews

4.5 rating, based on 2 Class Central reviews

Start your review of Bifurcation Theory - Saddle-Node, Hopf, Transcritical, Pitchfork

  • Profile image for LE Truong Hai
    LE Truong Hai @TruongHai
    This is a very good sumarizationf for types of bifurcation. Having watched all the videos, I got an overview of bifurcation technique which is critical for my research. However, this course seems to be a small part of a bigger lecture. It is good if there is some hints in this course which guide me to the previous part of this lecture so that I can gain a smooth flow of knowledge.
  • Muhammad Majid
    I truly enjoyed this course.” “I appreciated how the instructor surveyed the class before to get a sense of what we all wanted to take away from the course.” “The instructors were fantastic – very knowledgeable and willing to answer questions as they came up
Start learning

Never Stop Learning.

Get personalized course recommendations, track subjects and courses with reminders, and more.

Sign up for free
Someone learning on their laptop while sitting on the floor.