Activity for Alois Steindl
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Alois Steindl posted a comment on ticket #55
Sorry, I missed to attach the input file in the first post. Here it comes. With kind wishes Alois
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Continuation of a P2-orbit in an non-autonomous ODE: How to deal with the gluing conditions
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Dear MatCont team, first of all: Merry Christmas, Happy New Year and a quiet and comfortable holiday time! I encountered some problems when playing (again) around with the Mathieu equation: Fixing the excitation amplitude and varying the excitation frequency ny along the trivial solution the program locates the period doubling points and some BPCs, where the Floquet multiplier becomes 1. When trying to find the BPCs in the (a, ny) plane, MatCont throws the error "Not enough input arguments". I guess...
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Hello, it is still not clear, what you tried to do: After you obtained the approximate limit cycle, did you tell MatCont, that you are looking for limit cycles? (I think, MatCont automatically selects that choice, after it finds the approximate circle.) Did you select a proper bifucation parameter? Looking at your parameters: w is quite close to w1 and w2. You could try to start at e.g. w=4 and decrease it. Since you have two quite similar modes, I would expect a lot of resonances near w=w1=w2. (PS.:...
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Hello, I am not a member of the Matcont team. Your description is quite vague: I guess you have rewritten your differential integral algebraic equation as some regular set of ordinary differential equations (or at least a set of n equations in n unknowns (and some parameters)). If you have found a regular solution (without zero eigenvalues), it should normally work to pass it to MatCont as initial guess and start a continuation. You might have to play around with some continuation settings (initial...
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Dear Harry,thank you very much for your kind response and the fast treatment of the problem, I am really impressed.I guess, that it is actually a fault in Matlab on Windows, because the help entry for strsplit in Matlab states that "The substrings specified in delimiter do not appear in the output newStr." so I think I should send a bug report.I am learning coco and could already find a family of periodic solutions containg BPCs and LPCs. I still have to get familiar with the details, but coco makes...
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You are guessing right, I use Matlab in Windows. I just tried your suggestion with strncmp and that also works. Thanks again for your efforts! Alois
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Dear Jan, thank you very much for your patient treatment of the problem! I put a breakpoint at the end of funend and could observe, that the treatment of the newline character in string functions might be the problem: After splitting the string at the newlines, the newline character remains in the strings, so one gets 'end\n' (actually Matlab 2023b distinguishes between the placeholder '\n' and the actual newline character <nl>, so the second last entry in str is 'end<nl>'. Therefore strcmp gives...
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Dear Jan, thank you very much for your quick and helpful response! I downloaded and installed the new coco version on August 19; today I downloaded it again and the zip-files are identical. Still I get the error message with both Matlab 2023a and 2023b. I will try to find out what happens during the day. With kind regards Alois
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symcoco: syntax error in Matlab 2023b
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I think, that the description in the very first contribution in this thread describes the situation quite well; at least I recognized the reported problem as a quite well known one. When I played around yesterday, I could see, that from the same BPC it is possible, that MatCont finds the second branch without problems, after some trial and error with different settings, or not at all. In my first attempt I also could obtain the bifurcating branch immediately. If I find some time, I will try to debug...
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Dear Hil, thanks for the helpful response! Indeed, there was a typo in my post. The strange thing is, that after compiling the system, I get the error message. But the m-file is build correctly and it works. Maybe it has something to do with the new Matlab version, I installed recently. With kind regards Alois
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Hello Hil, I just retried my attempts from yesterday. I could find the branch of periodic solutions and (beside other interesting points like LPC and NS) a BPC close to n=2.02. But today it seems impossible to continue from there. I played around with TSearchOrder and Moore-Penrose, MinStepsize, initStepsize, no success. In the Matlab command window I get the messages first point found tangent vector to first point found Current step size too small (point 1) elapsed time = 7.1 secs npoints curve...
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Just a remark concerning my own post: It seems, that the system somehow garbles the contributions: In my case the *-signs (multiplication symbols; in case it happens again) vanish, which makes the formulas looking quite unreadable.
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Up to now it was possible, to use local variables, when writing the equations of motion. So instead of writing v'=-nyw + (lambda - v^2 - w^2)v w'=nyv + (lambda - v^2 - w^2)w it was possible to write lamh=lambda - v^2 - w^2 and later (in the early days it was even possible to specify such local values in between the equations) v'=-nyw + lamhv w'=nyn+lamhw Since yesterday I observe a Matlab error: "Free variable 'lamh' must be included in 'Vars' value." Has that been changed recently in MatCont (I...
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Dear Guilherme, I tried to input your equations; since there are no spaces displayed in the posting, I am not sure I got it right. After locating one periodic solution, I could follow the branch and saw a BPC close to n=2.02. In order to follow the bifurcating branch from there, I had to switch off TSearchOrder in the Continuer window. Please beware: Playing around, I got very different behaviours of the system. So either I made a severe mistake in trying to enter the equations, or the system is...
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Hello, as far as I know, MatCont doesn't deal with symmetries at all. One possible method would be to introduce symmetry breaking terms, the coefficients of these terms would be considered as imperfections. Look at the pizchfork bifurcation x'=x^3-lambdax with mirror reflection symmetry x-> -x. The branch point at (0,0) can be seen as regular branchpoint in the perturbed system x'=x^3-lambdax+alpha. While this method is cumbersome, when you are only interested in the symmetric case, it pays off when...
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Hello Jan, as Hil pointed out, MatCont isn't designed for treating quasiperiodic excitations/solutions. You would either need some other package or apply some simplification (e.g. averaging) to get rid of a frequency. You can of course vary the Hopf bifurcation parameter to study the influence of the excitation magnitude. Good luck Alois
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Hello, introducing a pair of equations, as you mentioned it in your second question, might not be the only way, but it is certainly a good one. You have of course to be aware, that you might obtain solutions with some phase shift. Another possibility would be to use MatContM, for which you would itegrate your equations over a period (or over multiple periods). Good luck Alois
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Hello Nathan, just 2 ideas, which might help: Try to call matcont clean or matcont clean reset from the matcont directory. If that doesn't help: Try to download and install matcont again, maybe some files got lossed or are corrupted. Good luck Alois
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Thanks Hil, that seems to be the most likely explanation of that behaviour. Irene could test it by trying to create some file or folder in the subdirectory Systems of her MatCont directory. When installing MatCont, was it necessary to have Administrator privileges? (While writing this, I am wondering, how this error would show up: Does the system already try to create the files, when the user types the name of the project?) In any case, if the MatCont directory lies in some restricted area, it should...
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Hello, the behaviour sounds really strange and I am wondering what might go on. One wild guess would be, that some file got damaged, either in the MatCont package or in the Matlab installation. That could be caused by some error in the file system. (These are quite rare, but they do happen.) It could be found by checking the file system. That can be called by chkdsk (or from the Windows explorer by right clicking on a drive -> Tools -> Error checking). If you already tried to run MatCont from a different...
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Hello, your error sounds really strange, I never encountered that one. (I am used to receive a lot of error messages.) I would suggest that you download Matcont again and install it in some other place. You could also try to get access to a Matlab installation on another computer. What is your computer OS? Another idea, if nothing else helps, would be to perform a file system check. Or you could try it from a different account. Are you experienced with debugging? You could also set a breakpoint at...
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Hello, if your simulations indicate small oscillations, then these oscillations do occur in the numerical formulation and matcont will have to take them into account. I would bet that your system is vulnerable to round-off errors or something similar happens. It would certainly be necessary to non-dimensionalize the model and rescale it, such that (in the ideal case) all quantities are of order 1 and also the equations contain expressions of order 1. In your parameter list there occur very small...
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Hello, matcont treats only autonomous systems. There is a nice trick to make your system autonomous: Add the two equations co'=lambdaco - omegasi - (co^2 +si^2)co si'=omegasi+lambdaco - (co^2+si^2)si This system undergoes a supercritical Hopf bifurcation at lambda=0. If you follow the periodic solution until lambda=1, you obtain cos(omega t) and sin(omega t), quite likely with some phase shift, which doesn't matter here. Good luck Alois
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Hello, I just saw your message. For your optimal control problem MatCont is quite likely not the first choice, you simply need some boundary value problem solver. In Matlab the powerful packages bvp4c and bvp5c are available; these use a collocation method. There should also exist some shooting methods. Good luck Alois
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Hello, I just read your question, so maybe you already found a solution. If you still have trouble with the userfunction, you could look at the .m-file of your project, the userfunction should appear quite in the last lines. Is pl the name of some parameter or variable? A wild guess: Newer versions of Matcont precede the parameter names by par_, so lambda becomes par_lambda. The change did not yet make it into the compilation for the userfunction. If the problem is still open, you could send me your...
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Hello, the error message sounds strange to me, but I am just a user of the package...
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I have meanwhile found the reason for this behaviour in the file gui_EP.m and could...
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I have meanwhile found the reason for this behaviour in the file gui_EP.m and could...
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I have meanwhile found one reason for that behaviour: The array gds.BranchParams...
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Hello, the meaning of these quantities is described on p17 of the Sep2012 Manual....
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Hello, what would you think about the equations y'=0 or y'=a*y^3 ? A personal hint:...
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Whenever I would like to plot say all imaginary parts of the eigenvalues along an...
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Hello, have a look at the eigenvalues: If all real parts are negative, the equilibrium...
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Subscripted assignment dimension mismatch
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