At the bifurcation point of GH, l2 is NaN

[Jianbin Ding]

Hi,
When I calculate the Hopf bifurcation curve, I start from a Hopf bifurcation point and detect the HH (double Hopf) and GH (Generalized Hopf) bifurcation points. But at HH: (P11 * P22,theta,delta)=(1, 4.398365e-01, 9.033867E +00), (THETA,DELTA)=(NaN, NaN), and at GH: L2 =NaN. When I try to do the LPC calculation from the GH point, I am prompted that the input matrix cannot contain NaN. So I would like to ask: in this case, what parameters can I modify to avoid this problem?
By the way, when I detected the Hopf bifurcation point from the equilibrium point, the first Lyapunov coefficient was NaN, which was solved by setting the derivative of the system from "SSSNN" to "SNNNN". This time I also tried to change the setting of the derivative, but I could not solve the new problem.
My model has 5 degrees of freedom and 3 free parameters, and most of the parameter Settings in the process are the default values.

Thanks to everyone in advance.

Best regards,

Dingjianbin

[hilmeijer]

Dear Jianbin,

This is difficult to say without knowing more details.

It could be the accuracy but also system properties.

Can you provide a Minimal Working Example (MWE)?

Best, Hil

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From: Jianbin Ding dingjianbin@users.sourceforge.net
Sent: Tuesday, July 13, 2021 3:26 PM
To: [matcont:discussion]
Subject: [matcont:discussion] At the bifurcation point of GH, l2 is NaN

Hi,
When I calculate the Hopf bifurcation curve, I start from a Hopf bifurcation point and detect the HH (double Hopf) and GH (Generalized Hopf) bifurcation points. But at HH: (P11 * P22,theta,delta)=(1, 4.398365e-01, 9.033867E +00), (THETA,DELTA)=(NaN, NaN), and at GH: L2 =NaN. When I try to do the LPC calculation from the GH point, I am prompted that the input matrix cannot contain NaN. So I would like to ask: in this case, what parameters can I modify to avoid this problem?
By the way, when I detected the Hopf bifurcation point from the equilibrium point, the first Lyapunov coefficient was NaN, which was solved by setting the derivative of the system from "SSSNN" to "SNNNN". This time I also tried to change the setting of the derivative, but I could not solve the new problem.
My model has 5 degrees of freedom and 3 free parameters, and most of the parameter Settings in the process are the default values.

Thanks to everyone in advance.

Best regards,

Dingjianbin

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At the bifurcation point of GH, l2 is NaN

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[Jianbin Ding]

Hello hilmeijer,

First of all, thank you very much for your reply. Next, I will describe the calculation of the bifurcation in detail.
1. Equilibrium point calculation. Input model, as shown in figure. The model is highly nonlinear, especially the expression of Mkdelta, which is itself a piecewise function, and here I use the tanh function to conduct smooth approximation to it. Model derivative is set to "SNNNN". Then select type-> Initial point->point, and input the Initial values as: t=0, y1=0.02, y2=y3=y4=y5=0, Fz=230000, V=1, c1 =300. In the Integrator window, set the Interval to 20 and leave the rest of the parameters as defaults. Click Window/Output->Graphic->2D Plot, bring up the drawing Window, set the abscissa to t, ordinate to y1, and click Matcont-> Fit Range. Then start the calculation. Click Compute->forward. You will get an oscillation curve converging to zero, as shown in the figure.
2. Hopf bifurcation point detection. Select the last point of the previous time domain curve as the starting point and click Type->Initial Poin-> Equilibrium. In the Starter window, select V as the free parameter. In the Continuer window, set MaxNumPoints to 3000 in order to calculate a larger V range, leaving the rest of the parameters as default. Set the abscissa of the Plot2D window to V and the ordinate to Fz. Bring up the Numeric window for monitoring calculations. Click on the Compute - > forward. In the drawing window, click Matcont-> Fit Range. You will get two Hopf bifurcation points and click Stop to Stop the calculation. Click on the Compute - > backword. Three Hopf bifurcation points and one BP point are detected. Their information as shown in the figure.
3. Two-parameter bifurcation diagram calculation. Click the Hopf bifurcation point detected by the last set of balance curves, (V=3.8614671), as the initial point. Set the type of the curve to Hopf. Clear the drawing window. Let's keep the coordinates the same. In the Starter window, set V and Fz as the continuation parameters. In the Continuum window, set MaxStepSize to 500, MaxNumPoints to 30,000, and CheckClosed to 500. Click on the Compute - > forward. It's going to detect two Hh, two GH. Their information is shown in the figure.
Thanks!
Jianbin Ding

[Jianbin Ding]

The two parameter bifurcation diagram.