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Bifurcations in 2D, Part 1 - Introduction, Saddle-Node, Pitchfork, Examples

Ross Dynamics Lab via YouTube

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This lecture extends bifurcation analysis from one-dimensional to two-dimensional systems. It examines saddle-node, pitchfork, and transcritical bifurcations using nullclines, phase-space bottlenecks, eigenvalues, and a genetic regulatory network example.

Syllabus

Introduction to bifurcations of fixed points in 2D.
Saddle-node bifurcation in 2D intro.
Ghosts of fixed points and bottlenecks in phase space.
Saddle-node bifurcation based on nullcline intersections.
Saddle-node example, genetic regulatory network.
Bifurcations occur along 1-dimensional center manifold.
Pitchfork and transcritical bifurcations in 2D.

Taught by

Ross Dynamics Lab

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