Explore bifurcations in two-dimensional systems through this comprehensive 43-minute video lecture. Extend your understanding of one-dimensional bifurcations to 2D systems, where fixed points and closed orbits can be created, destroyed, or destabilized as parameters vary. Examine prototypical examples and a genetic regulatory system to grasp key concepts. Learn about saddle-node bifurcations, ghosts of fixed points, bottlenecks in phase space, and nullcline intersections. Investigate a saddle-node example in a genetic regulatory network and understand how bifurcations occur along a one-dimensional center manifold. Conclude with an introduction to pitchfork and transcritical bifurcations in 2D systems. Enhance your knowledge of nonlinear dynamics and chaos through this in-depth exploration of 2D bifurcations.
Bifurcations in 2D, Part 1 - Introduction, Saddle-Node, Pitchfork, Examples
Overview
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
