how ot undestand H_LC continuation

[strct]

Hello,

my system is quite complicated and there is still plenty of work to do. (see https://sourceforge.net/p/matcont/discussion/762215/thread/bf4901ec52/) Mainly on convergence issues, but I hope I will manage it with careful treatment.

However, I am encountering this phenomena. I am not changing any tolerance. I can run this

opt=contset(opt,'MaxStepsize',0.01);
opt=contset(opt,'MaxNumPoints',100);
opt=contset(opt,'Multipliers',1);
x1 = x_EP(1:N, s_EP(2).index) %Hopf occurence in EP continuation
p(ap) = x_EP(N+1,s_EP(2).index); %parameter
[x0,v0]=init_H_LC(@odefile,x1,p,1,0.1,20,4);
opt = contset(opt,'Adapt',0);
[xlc,vlc,slc,hlc,flc]=cont(@limitcycle,x0,v0,opt);

and I obtain attached LC continuation.

What is confusing me, is that, clearly there is requested number of LCs, but it is nearly impossible to get somewhere, because the stepsize is so tiny. Is possbile to change it? Is it necessary to proceed like this? What this behaviour of slow continuation indicates to me?

[hilmeijer]

In your other posts you have set in the options (opt) an InitStepsize that is really small. Are you still using that small initial step?

Try increasing it.

And as said before, rescaling of your equations might be necessary in order for the continuation to work.
If some quantities are really sensitive, then some steps might be slow.

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From: Jan Filip strc@users.sourceforge.net
Sent: Sunday, October 24, 2021 5:20 PM
To: [matcont:discussion]
Subject: [matcont:discussion] how ot undestand H_LC continuation

Hello,

my system is quite complicated and there is still plenty of work to do. (see https://sourceforge.net/p/matcont/discussion/762215/thread/bf4901ec52/) Mainly on convergence issues, but I hope I will manage it with careful treatment.

However, I am encountering this phenomena. I am not changing any tolerance. I can run this

opt=contset(opt,'MaxStepsize',0.01);
opt=contset(opt,'MaxNumPoints',100);
opt=contset(opt,'Multipliers',1);
x1 = x_EP(1:N, s_EP(2).index) %Hopf occurence in EP continuation
p(ap) = x_EP(N+1,s_EP(2).index); %parameter
[x0,v0]=init_H_LC(@odefile,x1,p,1,0.1,20,4);
opt = contset(opt,'Adapt',0);
[xlc,vlc,slc,hlc,flc]=cont(@limitcycle,x0,v0,opt);

and I obtain attached LC continuation.

What is confusing me, is that, clearly there is requested number of LCs, but it is nearly impossible to get somewhere, because the stepsize is so tiny. Is possbile to change it? Is it necessary to proceed like this? What this behaviour of slow continuation indicates to me?

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how ot undestand H_LC continuation

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