Quite a few bibliographical sources observe, that a branch point of equilibria is not an inherent codimension-1 bifurcation, and rather a codimension-2 special point. However, MatCont seems to be doing a pretty good job on detecting pitchfork bifurcations of equilibria as "BP", agreeing well with the underlying physical effects, and this bifurcation appears to be in the same hierarchy as the Limit point and the Andronov-Hopf point within the code.
So, could anyone offer an explanation on why branch points should be treated differently than the other two, or what is the numerical explanation behind this? Thank you
Last edit: lanast 2020-12-19
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A branch point of equilibria is indeed a codimension-2 special point. In generic dynamical systems it typically occurs only under variation of two parameters. However, it also appears in systems with a symmetry or equivariance under variation of a single parameter. Since such systems are very common in many applications, MatCont also detects branch points of equilibria under variation of a single parameter.
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One more comprehension question: for a system with symmetry, I am detecting a branch point of equilibria which appears to be equivalent to a pitchfork bifurcation. Is it possible to continue this point in a codimension-2 study in MatCont by variation of a second parameter?
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Yes, in most cases this would be possible, unless you have some additional restriction.
You may try to continue it as a Limit Point curve with two parameters.
Best, Hil
From: lanast lanast@users.sourceforge.net
Sent: Wednesday, January 6, 2021 11:03 AM
To: [matcont:discussion]
Subject: [matcont:discussion] Branch Point of equilibria, really codim-2 ?
One more comprehension question: for a system with symmetry, I am detecting a branch point of equilibria which appears to be equivalent to a pitchfork bifurcation. Is it possible to continue this point in a codimension-2 study in MatCont by variation of a second parameter?
Quite a few bibliographical sources observe, that a branch point of equilibria is not an inherent codimension-1 bifurcation, and rather a codimension-2 special point. However, MatCont seems to be doing a pretty good job on detecting pitchfork bifurcations of equilibria as "BP", agreeing well with the underlying physical effects, and this bifurcation appears to be in the same hierarchy as the Limit point and the Andronov-Hopf point within the code.
So, could anyone offer an explanation on why branch points should be treated differently than the other two, or what is the numerical explanation behind this? Thank you
Last edit: lanast 2020-12-19
A branch point of equilibria is indeed a codimension-2 special point. In generic dynamical systems it typically occurs only under variation of two parameters. However, it also appears in systems with a symmetry or equivariance under variation of a single parameter. Since such systems are very common in many applications, MatCont also detects branch points of equilibria under variation of a single parameter.
Thanks for this hint professor
One more comprehension question: for a system with symmetry, I am detecting a branch point of equilibria which appears to be equivalent to a pitchfork bifurcation. Is it possible to continue this point in a codimension-2 study in MatCont by variation of a second parameter?
Yes, in most cases this would be possible, unless you have some additional restriction.
You may try to continue it as a Limit Point curve with two parameters.
Best, Hil
From: lanast lanast@users.sourceforge.net
Sent: Wednesday, January 6, 2021 11:03 AM
To: [matcont:discussion]
Subject: [matcont:discussion] Branch Point of equilibria, really codim-2 ?
One more comprehension question: for a system with symmetry, I am detecting a branch point of equilibria which appears to be equivalent to a pitchfork bifurcation. Is it possible to continue this point in a codimension-2 study in MatCont by variation of a second parameter?
Branch Point of equilibria, really codim-2 ?
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