A Primer in Bifurcation Theory for Computational Cell
A Primer in Bifurcation Theory for Computational Cell Biologists Lecture 6: Takens-Bogdanov Bifurcation http: //www. biology. vt. edu/faculty/tyson/lectures. php John J. Tyson Click on icon to start audio Virginia Polytechnic Institute & Virginia Bioinformatics Institute
Cusp Bifurcation s s sxs Variable, x Parameter, q “universal unfolding” Parameter, p
Degenerate Hopf Bifurcation “universal unfolding” sup. HB CF s u sub. HB Variable, x Parameter, q s Parameter, p
sub. HB uxs s “universal unfolding” s xs s s sxs s SN Parameter, p x s x ulc SL Variable, x Parameter, q Takens-Bogdanov Bifurcation u Parameter, p s
Bistability & Oscillations in Chemical Reactors stirrer Pacault, Vidal, de. Kepper, Boissonade 1970’s, CNRS, Bordeaux France osc outflow Parameter, q inflow s s sxs Parameter, p “Cross-shaped Phase Diagram”
Toy Model l k SN sub. HB Guckenheimer (1986) Physica D 20: 1 -20
Saddle-Node Loop Bifurcation Parameter, q SN u u xs SNIC Parameter, p SL Variable, x uxs SLC u x s Parameter, p
Saddle-Node Loop & Takens-Bogdanov Bifurcations s s HB u xs sxs u SL TB SNL SNIC uxs Variable, x Parameter, q cusp s SN Parameter, p
Neutral Saddle-Loop Bifurcation CF SL SL
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