This course on Bifurcation Theory covers the following learning outcomes and goals: understanding qualitative changes in phase portraits for vector fields and maps as parameters vary, focusing on local bifurcation theory near fixed points, and discussing saddle-node, transcritical, pitchfork, and Hopf bifurcations. The course teaches skills in analyzing bifurcations, identifying stability changes in fixed points, and generating periodic orbits from fixed points. The teaching method includes lectures with theoretical explanations and examples. The intended audience for this course includes students and professionals interested in nonlinear dynamics, dynamical systems, mathematics, and chaos theory.
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
