strct

Hello everyone, following Meijer's notes on his website I performed some analysis of forced system. below is shown a sketch of the situation. If I obtain Neimark-Sacker curve (denoted NS) a also detect several resonances + Chenciner between them. From R1 points, I can initiate continuation of fold cycles LPC giving rise to correct Arnold tongue as is shown below. For some R1 points however I obtain and elliptic closed curve as is shown leftomost of the figure. Is this even correct? Because than it...

Hello, can we access stability color highlighting in cpl routine programatically? I usually go through all eginevalues myself to check if everything fits, but it would be nice to have this feature for agile testing sessions. Is there an easy option how to use this feature as I was not able to find this documented. Jan

Thank you for your kind replies both of you. This is actaully very good point. I am about to introduce the excitation as shown in attachement. That is quite difficult. I came up with two approaches. 1/ take its Fourier series up to some finite term, but this would require harmonics of order 15 in most applications. First I need to get at leat one normal form. Higher harmonics of order n could be obtained using T_n(cos(wt)), where T_n is a Chebyshev polynomial of the 1st kind of order n. But the coefficients...

Hello, thank you, Alois. Normal form approach works pretty well. Jan

Hello, thank you, Alois. Normal form approach work very well. Jan

Hello, thank you Alois. I am aware that there has been already question regarding multiharmonic forcing with cos(nwt). Approach suggested by Meijer was the use of trigonometric identities to obtains such signals. As I understand it, to get cos(nwt) universally I can use Chebyshev polynomials T_n(cos(wt))=cos(nwt) but coefficients of these polynomials are getting really high for high order. As this problem is really useful I think this might help others as well: Question 1: If I introduce forcing...

To be more concrete, let me show this very simple example. I am following manual and using initOrbLC routine. Even if time integration seems to work good and the limit cycle is nice circle (screen attached) I cannot get convergence at cont routine p=[A,w,R,L,C]; ap=[1]; tolerance=1e-2; [x0,v0]=initOrbLC(@excitePi,t,y,p,ap,20,4,tolerance); opt=contset; opt=contset(opt,'MaxNumPoints',50); [xlcc,vlcc,slcc,hlcc,flcc]=cont(@limitcycle,x0,v0,opt); The system is nonautonomous, therefore I introduce it as...

1/ In textbooks, you can often find trick how to turn ODE system with external forcing A cos(wt) by introducing another variable y and putting its derivative equal to one. This is working pretty much good on paper, but is this a proper and working way how to prepare nonautnomous ODE for MatCont? Because, as I understand, input format require time derivatives on the left-hand side . How MatCont can recognize two variables y and t which are basically the same but introduced in completely different...