Physical examples of different types of bifurcation

[Jezza]

I have to sit an exam on non linear dynamical systems in a couple of weeks. Something that's been asked in the past is to name physical examples of different types of bifurcation. I've consulted Strogatz's book and the internet to try and find some, but I can't seem to find many (or even any) physical examples for all the different types.

What I've got so far is (These are the types we have to know about):

• Saddle node - a driven pendulum; the bifurcation occurs when the torque is sufficient to push the pendulum over the top.
• Transcritical - A laser amplifier reaching the critical level of pumping to produce a population inversion.
• Supercritical pitchfork - The onset of Rayleigh-Benard convection.
• Subcritical pitchfork - I think I've heard about something the reaction that tells the heart to pump?
• Supercritical Hopf - No ideas.
• Subcritical Hopf - The transition to chaos in the Lorenz system i.e. Rayleigh-Benard convection.

In particular, a recent exam question asked for examples of Hopf bifurcations (of either type) in fluid systems, so another example specific to fluids in this case would be ideal.

Examples related to fluids/and or biological systems would be particularly good because fluids, non linear systems and biological physics are all lumped into one exam!

 

[Andy Resnick]

I have to sit an exam on non linear dynamical systems in a couple of weeks. Something that's been asked in the past is to name physical examples of different types of bifurcation. I've consulted Strogatz's book and the internet to try and find some, but I can't seem to find many (or even any) physical examples for all the different types.

What I've got so far is (These are the types we have to know about):

• Saddle node - a driven pendulum; the bifurcation occurs when the torque is sufficient to push the pendulum over the top.
• Transcritical - A laser amplifier reaching the critical level of pumping to produce a population inversion.
• Supercritical pitchfork - The onset of Rayleigh-Benard convection.
• Subcritical pitchfork - I think I've heard about something the reaction that tells the heart to pump?
• Supercritical Hopf - No ideas.
• Subcritical Hopf - The transition to chaos in the Lorenz system i.e. Rayleigh-Benard convection.

In particular, a recent exam question asked for examples of Hopf bifurcations (of either type) in fluid systems, so another example specific to fluids in this case would be ideal.

Examples related to fluids/and or biological systems would be particularly good because fluids, non linear systems and biological physics are all lumped into one exam!

Supercritical Hopf:
https://www.researchgate.net/publication/265526362_TRANSITION_TO_CHAOTIC_MARANGONI_CONVECTION_IN_LIQUID_BRIDGE
http://adsabs.harvard.edu/abs/2004PhFl...16.1746M

Others:
https://www2.cose.isu.edu/~palmbenn/pdf/BifurcationStability.pdf.
https://www.google.com/url?sa=t&rct...50008124.pdf&usg=AOvVaw13Iq6wwd6VHnZu3-1R0KJ3