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Hopf bifurcation for vector fields and maps, the generation of periodic orbits out of fixed points
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Classroom Contents
Bifurcation Theory - Saddle-Node, Hopf, Transcritical, Pitchfork
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- 1 Local Bifurcation Theory
- 2 System in n dimensions, only look at center manifold directions
- 3 saddle-node bifurcation,
- 4 transcritical bifurcation,
- 5 pitchfork bifurcation,
- 6 period-doubling bifurcation for maps, related to the period doubling cascade (it's like a pitchfork bifurcation for maps)
- 7 Hopf bifurcation for vector fields and maps, the generation of periodic orbits out of fixed points
