Physical examples of different types of bifurcation

In summary, the conversation was about the speaker's upcoming exam on non-linear dynamical systems and their search for physical examples of different types of bifurcation. They have consulted sources such as a book by Strogatz and the internet, but have not found many examples. They mention the types of bifurcation they have learned about so far, including saddle node, transcritical, supercritical and subcritical pitchfork, and supercritical and subcritical Hopf. They also mention a recent exam question asking for examples of Hopf bifurcations in fluid systems and express a preference for examples related to fluids and/or biological systems. They provide some potential examples, including chaotic Marangoni convection and bifurcation stability, but express
  • #1
Jezza
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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!
 
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  • #2
Jezza said:
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
 

Related to Physical examples of different types of bifurcation

1. What are the different types of bifurcation?

There are three main types of bifurcation: saddle-node, transcritical, and pitchfork. These can be further classified into subtypes based on the number of parameters involved and the direction of the bifurcation.

2. What is a saddle-node bifurcation?

A saddle-node bifurcation occurs when a stable fixed point and an unstable fixed point collide and annihilate each other, resulting in the loss of the fixed point and the creation of a limit cycle.

3. Can you give an example of a pitchfork bifurcation?

One example of a pitchfork bifurcation is the formation of vortices in a fluid flow. As the flow rate increases, the behavior of the fluid changes from a stable, laminar flow to an unstable, oscillating flow.

4. How are bifurcations relevant in real-world systems?

Bifurcations are relevant in many real-world systems, such as weather patterns, population dynamics, and chemical reactions. They can lead to sudden and dramatic changes in behavior, making them important to understand in order to predict and control these systems.

5. Can bifurcations be controlled or avoided?

In some cases, bifurcations can be controlled or avoided by adjusting the system parameters. However, in complex systems, it may be difficult to predict and control the occurrence of bifurcations, making them a challenge for scientists and engineers.

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