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'Current step size too small '- Continuation from Hopf bifurcation to find limit cycles

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vr98
2020-01-01
2023-09-11

  • vr98

    vr98 - 2020-01-01

    Hello
    I have a 11 state variable system analysed with respect to one active parameter. After continuation and obtaining bifurcation points I am attempting to find limit cycles.
    I have initialized my system at a Hopf bifurcation and to find limit cycles. After computing a few limit cycles, I get the following message

    'Current step size too small '
    And no more limit cycles are computed.

    • I have tried increasing stepsizes and tolerances. But the error persists.

    • I have tried to initialize at the last limit cycle that MatCont computes and try to move further, but that also gives the same error.
      No bifurcation points are reported on the limit cycles like limit points etc. Which means it cannot be stopping further limit cycle computation due to the presence of a codim 2 bifurcation I presume.

    • What does this message mean exactly?

    • Does it mean no more limit cycles exist?
    • If they do exist, what can I do to compute further limit cycles?

    Thank you!

     

    • hilmeijer

      hilmeijer - 2020-01-06

      1 This means your numerical problem has become too difficult to solve: The Newton iterations do not converge anymore.

      2 You can't say no more cycles exist without further study.

      3 Use more meshpoints to improve the discretization of the cycle. (But keep ncol=4) (setting Adapt=0 sometimes helps as well)

      From: vr98 vr98@users.sourceforge.net
      Sent: Wednesday, January 1, 2020 5:59 AM
      To: [matcont:discussion]
      Subject: [matcont:discussion] 'Current step size too small '- Continuation from Hopf bifurcation to find limit cycles

      Hello
      I have a 11 state variable system analysed with respect to one active parameter. After continuation and obtaining bifurcation points I am attempting to find limit cycles.
      I have initialized my system at a Hopf bifurcation and to find limit cycles. After computing a few limit cycles, I get the following message

      'Current step size too small '
      And no more limit cycles are computed.

      • I have tried increasing stepsizes and tolerances. But the error persists.

      • I have tried to initialize at the last limit cycle that MatCont computes and try to move further, but that also gives the same error.
        No bifurcation points are reported on the limit cycles like limit points etc. Which means it cannot be stopping further limit cycle computation due to the presence of a codim 2 bifurcation I presume.

      • What does this message mean exactly?

      • Does it mean no more limit cycles exist?
      • If they do exist, what can I do to compute further limit cycles?

      Thank you!

      'Current step size too small '- Continuation from Hopf bifurcation to find limit cycles

      Sent from sourceforge.net because you indicated interest in https://sourceforge.net/p/matcont/discussion/762214/

      To unsubscribe from further messages, please visit https://sourceforge.net/auth/subscriptions/

       
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  • Rajni Kant Kumar

    Rajni Kant Kumar - 2022-05-07

    I was drawing a bifurcation diagram for a beam absorber model where I have stuck in getting hopf bifurcation diagram. An error message comes ('No convergence at x0'). I have followed the same procedure to get the hopf bifurcation as written in a tutorial named ('Two-parameter bifurcation analysis of equilibria and limit cycles with matcont') but unable to draw for my model. Can anybody have solution of my problem? please help.

    One more problem arises when I increase the forcing amplitude of my ODE, where the continuation stopped by showing an error ('the current step size is too small'). what I have to do.

     

    • hilmeijer

      hilmeijer - 2022-05-09

      Dear Rajni,
      Saying there is an "error", without technical details, is pretty vague for others.
      It depends so much on the system, and possibly the way you defined the system in MatCont.
      As indicated before on the forum, we need details to answer this. Please provide so.
      Best regards, Hil Meijer

      Van: Rajni Kant Kumar rajni1234@users.sourceforge.net
      Verzonden: zaterdag 7 mei 2022 13:13
      Aan: [matcont:discussion] 762214@discussion.matcont.p.re.sourceforge.net
      Onderwerp: [matcont:discussion] 'Current step size too small '- Continuation from Hopf bifurcation to find limit cycles

      I was drawing a bifurcation diagram for a beam absorber model where I have stuck in getting hopf bifurcation diagram. An error message comes ('No convergence at x0'). I have followed the same procedure to get the hopf bifurcation as written in a tutorial named ('Two-parameter bifurcation analysis of equilibria and limit cycles with matcont') but unable to draw for my model. Can anybody have solution of my problem? please help.

      One more problem arises when I increase the forcing amplitude of my ODE, where the continuation stopped by showing an error ('the current step size is too small'). what I have to do.

      'Current step size too small '- Continuation from Hopf bifurcation to find limit cycles

      Sent from sourceforge.net because you indicated interest in https://sourceforge.net/p/matcont/discussion/762214/

      To unsubscribe from further messages, please visit https://sourceforge.net/auth/subscriptions/

       
      alternate

  • Swastika

    Swastika - 2023-09-11

    Hi Hil,
    I extended BT point in an effort to find the homoclinic curve. A small Hom curve was plotted when the value of adapt was 3.I verified that Matlab creates a homoclinic loop. I was unable to extend the Hom curve, though. It said that the "Current step size too small" prevented me from extending it.
    As a result, when I set adapt to 0, a homoclinic loop was produced, though it differed from the previous hom curve. I verified that it doesn't produce a homoclinic loop using the phase portrait diagram.

    Please provide a method for creating a hom curve that is accurate and extendable.

     

    • hilmeijer

      hilmeijer - 2023-09-11

      Dear Swastika,

      If you think the homoclinic predictor is not good enough, may I kindly point you to https://arxiv.org/abs/2109.12570. This is the method incorporated into MatCont.

      That said, homoclinic continuation itself is not trivial and requires quite some experience and insight into the dynamics. Most importantly, the any choice of period, eps0 and eps1 (one or two out of these three) could work. The way you pose your problem it is impossible to state what one should do.

      Best regards,
      Hil Meijer

      Van: discussion@matcont.p.re.sourceforge.net discussion@matcont.p.re.sourceforge.net namens Swastika swastika@users.sourceforge.net
      Verzonden: maandag 11 september 2023 13:33
      Aan: [matcont:discussion] 762214@discussion.matcont.p.re.sourceforge.net
      Onderwerp: [matcont:discussion] 'Current step size too small '- Continuation from Hopf bifurcation to find limit cycles

      Hi Hil,
      I extended BT point in an effort to find the homoclinic curve. A small Hom curve was plotted when the value of adapt was 3.I verified that Matlab creates a homoclinic loop. I was unable to extend the Hom curve, though. It said that the "Current step size too small" prevented me from extending it.
      As a result, when I set adapt to 0, a homoclinic loop was produced, though it differed from the previous hom curve. I verified that it doesn't produce a homoclinic loop using the phase portrait diagram.

      Please provide a method for creating a hom curve that is accurate and extendable.

       
      alternate

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