Explore the intricacies of bifurcation theory in this comprehensive lecture from Dr. Shane Ross's course on 'Center manifolds, normal forms, and bifurcations'. Delve into local bifurcation theory near fixed points, examining qualitative changes in phase portraits as parameters vary. Focus on one-dimensional center manifolds and learn about saddle-node, transcritical, pitchfork, and period-doubling bifurcations. Gain insights into the Hopf bifurcation for vector fields and maps, understanding how periodic orbits emerge from fixed points. Discover which bifurcations are robust to perturbations and how they apply to equilibrium points of vector fields and periodic orbits.
Bifurcation Theory - Saddle-Node, Hopf, Transcritical, Pitchfork
Overview
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
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Reviews
4.5 rating, based on 2 Class Central reviews
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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.
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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
