Continuation Core and Toolboxes (COCO) / Tickets / #42 Switching between solution branches at a BP point

#42 Switching between solution branches at a BP point

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Status: open

Owner: nobody

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Updated: 2018-03-05

Created: 2018-02-28

Creator: Jacob Enciu

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I am trying to switch branches at a fork bifurcation branch point. COCO first tracks the center branch back from the BP point, and only then starts again fron the BP and switches to the second branch.
My dynamic model has been previously analyzed using AUTO (with Dynamic System Tools) and validated by tests.
Fig. 1 shows the two branches: centerline branch and asymmetric branch. The data shows the yaw angle of an aerodynamic load as a function of airspeed, where airspeed is the continuation parameter.
Fig. 2 only shows the second branch produced following the command:
prob2 = ode_BP2ep(prob2,'', 'CenterBranch',labs_BP(1),'-switch');
where 'CenterBranch' hold the solution for the center branch, and labs_BP(1) is the label of the branch point. The '-switch' flag does not seem to have an effect.

The attached files are as follows:
workspace.mat - MATLAB workspace
coco_log1.txt - log file for 'CenterBranch'
coco_log2.txt - log file for 'BP1_U' - second branch (switching from BP at v=144.2 ft/s)

5 Attachments

Fig1.fig

Fig2.fig

coco_log1.txt

coco_log2.txt

workspace.mat

Discussion

Harry Dankowicz - 2018-03-05

Hi Jacob,

Working backwards:

You can get help with the ode_BP2ep constructor syntax by typing 'help' followed by 'ode_BP2ep' on the command line. As you can see, there is no '-switch' option for this constructor. Your observation about the fact that inclusion of '-switch' has no effect is consistent with the expected behavior.

The branch switching routine is using an initial solution guess that is displaced a small distance from the (approximately located) branch point along a vector that is perpendicular to the original branch and in the plane of both solution branches. The projection condition should ensure that we don't fall back onto the original branch.

It is curious that the algorithm is able to locate the secondary branch when perturbing in one direction, but not the other. Is there a nonsmoothness in your governing vector field at \psi=0?

For me to provide further assistance, I would need access to all the files required to run this example.

Harry
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Switching between solution branches at a BP point

Toolboxes for parameter continuation and bifurcation analysis.

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#42 Switching between solution branches at a BP point

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