yet another "No convergence at x0"
Numerical Bifurcation Analysis Toolbox in Matlab
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Dear all,
I am trying to do a bifurcation analysis on the Diekman2013 model. The model describes a SCN neuron (clock neuron) as a combination of a Hodgking Huxley model and a Goodwin model. It is in the attechmets. The first state describes the membrane voltage. States 2 through 8 represent the gating variables. State 9 and 10 represent calcium concentrations coupling the electrical part with the genetic clock of states 11, 12 and 13.
I am interested in the case of synchronisation between to neurons. However, so far I have not even been able to get a one neuron model past the "no convergence at x0" error. So I will focus on that first. The original model has quite a lot of constantes, so for conveniece I filled their values in and used a dummy bifurcation parameter a.
Subsequently, I let the system approach the limit cycle. The timescale is in miliseconds. Period is about 78500000 which roughly corresponds to the daylength 24360010^3. I let the model do one cycle. Subsequently I select this curve by clicking "select/curve" in the "matcont" window. In the "starter" window that pups up I click "select curve". In the starter window I select parameter a and the period and click compute forward. After a minute or so the error "no convergence at x0" pups up.
Is there anything else I can do except getting even closer to the limit cycle? I already let it run for hours on a small stepsize. Or am I doing something else wrong? I am a little but out of ideas here. Thanks for your help
Kind Regards,
Oscar
Dear Oscar,
I won't go into a detailed study of your model, but there are a few steps you can consider.
(1) This routine to start up a limit cycle requires that you start on the cycle, and then simulate for just a little more than one period. If the orbit still contains transients then subsequent Newton iterations may not be enough to find the cycle.
(1a) The parameter a is not entirely artificial as you multiply the final equations with it. What is the value of a? You supply the model but the state is needed too for someone to check it.
(2) The discretization of the orbit may not be good enough. The period you mention is quite high, while if there is fast neuronal dynamics as well there may be many events. I'm not sure that this will work. You could have a look at the file Continuer/newtcorr.m and then add on line 49: [norm(dx) norm(Q)] so that you can inspect the performance of the corrections. If both dx and Q are large, then you may either need more points, or something else.
Best regards, Hil Meijer
From: OscarHT oscarht@users.sourceforge.net
Sent: Thursday, February 28, 2019 11:13 AM
To: [matcont:discussion]
Subject: [matcont:discussion] yet another "No convergence at x0"
Dear all,
I am trying to do a bifurcation analysis on the Diekman2013 model. The model describes a SCN neuron (clock neuron) as a combination of a Hodgking Huxley model and a Goodwin model. It is in the attechmets. The first state describes the membrane voltage. States 2 through 8 represent the gating variables. State 9 and 10 represent calcium concentrations coupling the electrical part with the genetic clock of states 11, 12 and 13.
I am interested in the case of synchronisation between to neurons. However, so far I have not even been able to get a one neuron model past the "no convergence at x0" error. So I will focus on that first. The original model has quite a lot of constantes, so for conveniece I filled their values in and used a dummy bifurcation parameter a.
Subsequently, I let the system approach the limit cycle. The timescale is in miliseconds. Period is about 78500000 which roughly corresponds to the daylength 24360010^3. I let the model do one cycle. Subsequently I select this curve by clicking "select/curve" in the "matcont" window. In the "starter" window that pups up I click "select curve". In the starter window I select parameter a and the period and click compute forward. After a minute or so the error "no convergence at x0" pups up.
Is there anything else I can do except getting even closer to the limit cycle? I already let it run for hours on a small stepsize. Or am I doing something else wrong? I am a little but out of ideas here. Thanks for your help
Kind Regards,
Oscar
yet another "No convergence at x0"
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