SelectCycle

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2012-01-19
2015-08-28
  • Maurizio De Pitta'

    Dear all,
    I need to start start the continuation of periodic orbits from curves computed by time integration.
    In my system I first compute with stringent Abs and Rel tolerance values a periodic solution, and then I use the "SelectCycle" button in the Starter window.

    In the Matcont window at this point, the curve type changes from P_O to LC_LC and in the Starter window again I select two parameters, typically my bifurcation parameter and the Period. Then in the dialog box that appears where I am asked what tolerance I want to locate the cycle, I tried to use both teh default value (i.e. 1e-2) or more stringent tolerances (i.e. 1e-6).

    In both cases though the continuation fails because there is "No convergence in x0".

    How can I be sure that I get convergence in x0 and thus start the continuation?
    My time solution, was computed in a time interval of 100s with stable oscillations with typical period of 1s and RelTol and AbsTol around 1e-8.

    Thank you in advance. Any help will be appreciated.
    Looking forward your advices.

    Best,
    Maurizio

     
  • Henry Mattingly

    Henry Mattingly - 2015-08-28

    Sorry to get to you so late Maurizio. I had the problem of "No convergence in x0." once before when it wasn't clear how that could be.

    It turns out that if the Jacobian of your system contains a zero eigenvalue (such as in the case of chemical kinetics when there is a conservation law, making one of your species linearly dependent on the others), then you cannot do continuation and you will get this error. If your system has a state variable that is linearly dependent on the others and can be eliminated, that might take care of the problem.

    Henry

     

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