Dear Fellows
Hello
I am Qasim, presently undergoing thesis phase of my MS. I am using “Matcont” for my thesis.
I am facing some problems regarding matcont. I am using an 11th order system (11 first order differential equations). The problem starts when I try to start “Continuation”. Mat cont gives me the message “No convergence at x0”. I have confirmed that the initial conditions input in the “Starter” window really correspond to an equilibrium condition. I have confirmed it in the following 02 ways:
(a) I have found the derivatives, and these are really zero (of the order of 10-3) i.e. my chosen equilibrium point is an equilibrium point in real terms.
(b) Time based simulations starting from the chosen equilibrium point converge in an ideal manner.
I am interested to know that what else may be the reason for the error message “No convergence at x0”. I have chosen to calculate all derivatives numerically in the system definition window. I have already played with the different tolerance values in the “Continuer” window, and chosen different integration methods like ode45, ode23s etc. but the problem still persists. I am using Matcont version 2.5.1 with Matlab 7.0.4.
As till the time I don’t solve this problem, I can’t start with the ‘Continuation’. If someone may guide me in this issue, I would be highly obliged.
Thanks a lot
Best regards
Qasim
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I suggest that you try the following: start a time integration of your system from your approximate equilibrium until you clearly see that the coordinates no longer change. Then use the Select-Initial point button on the main MatCont window to select the last point of the computed orbit. Then declare the curve type as equilibrium, select the free parameter and try to start the continuation.
Let me know what happens,
Best regards,
Willy Govaerts
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Thanks for your guidance. Update on the faced problem of “No convergence at x0” is as follows:
(a) I started time integration from the equilibrium point for t=120. Very slight changes from the input initial conditions were observed. I chose last point of the computed orbit while declaring it as my equilibrium point. I tried to perform ‘Equilibrium continuation’ while selecting a free parameter. I again saw the same message “no convergence at x0”.
(b) I tried to perform equilibrium continuation in the command line version of matcont (cl_matcont). But error dialogue box for “No convergence at x0” was again seen.
(C) I changed my free parameter (I have five parameters and 11 states in total). To my amazement, I was fortunate to see the message “first point found; tangent vector to first point found” in the command window of matlab. I found that I was able to get bifurcation diagrams while selecting either of two parameters as my active parameters (out of five). For the rest of three parameters, when I choose either of these as my active parameters, I get the message “No convergence at x0”. It was further noticed that bifurcation diagrams were computed only for those parameters whose values were very small (almost zero) at the initial equilibrium point. Can some one explain this phenomenon?
(d) The two bifurcation diagrams were not much informative as one was a simple straight vertical line i.e. matcont did not change the value of free parameter and I was getting different values of a particular state for one value of my active parameter. Any comments please?
(e) My 2nd bifurcation diagram was a simple a dot. Does it indicate that no adjacent equilibrium point exists for my initial chosen equilibrium point?
I am using Matcont version 2.5.1 with Matlab 7.0.4 on Windows XP professional version 2002 service pack2.
Your valuable guidance is solicited.
Thanking you in anticipation
Best regards
Qasim
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I have started the time integration point from a Bogdanov Takens Point, with the interest of finding the hopf curve. But I again saw the same message "No convergence at x0".
Valuable guidance is desired.
Thanks.
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Hi, this is confusing. Time integration is not what you would do for finding a Hopf bifurcation curve. Instead you start continuation Initial point type "BT" and curve type "H(opf)". If that fails, you start slightly away from the BT point, to detect the Hopf point from equilibrium continuation.
If you would like to refer to this comment somewhere else in this project, copy and paste the following link:
Dear Fellows
Hello
I am Qasim, presently undergoing thesis phase of my MS. I am using “Matcont” for my thesis.
I am facing some problems regarding matcont. I am using an 11th order system (11 first order differential equations). The problem starts when I try to start “Continuation”. Mat cont gives me the message “No convergence at x0”. I have confirmed that the initial conditions input in the “Starter” window really correspond to an equilibrium condition. I have confirmed it in the following 02 ways:
(a) I have found the derivatives, and these are really zero (of the order of 10-3) i.e. my chosen equilibrium point is an equilibrium point in real terms.
(b) Time based simulations starting from the chosen equilibrium point converge in an ideal manner.
I am interested to know that what else may be the reason for the error message “No convergence at x0”. I have chosen to calculate all derivatives numerically in the system definition window. I have already played with the different tolerance values in the “Continuer” window, and chosen different integration methods like ode45, ode23s etc. but the problem still persists. I am using Matcont version 2.5.1 with Matlab 7.0.4.
As till the time I don’t solve this problem, I can’t start with the ‘Continuation’. If someone may guide me in this issue, I would be highly obliged.
Thanks a lot
Best regards
Qasim
I had similar problem, with 4 equations system. I believe that nonlinearity of the system was a problem. See:
I finaly started using AUTO, there was no such problems.
: https://sourceforge.net/projects/matcont/forums/forum/762214/topic/2656234
Dear colleague,
I suggest that you try the following: start a time integration of your system from your approximate equilibrium until you clearly see that the coordinates no longer change. Then use the Select-Initial point button on the main MatCont window to select the last point of the computed orbit. Then declare the curve type as equilibrium, select the free parameter and try to start the continuation.
Let me know what happens,
Best regards,
Willy Govaerts
Dear Sir
Thanks for your guidance. Update on the faced problem of “No convergence at x0” is as follows:
(a) I started time integration from the equilibrium point for t=120. Very slight changes from the input initial conditions were observed. I chose last point of the computed orbit while declaring it as my equilibrium point. I tried to perform ‘Equilibrium continuation’ while selecting a free parameter. I again saw the same message “no convergence at x0”.
(b) I tried to perform equilibrium continuation in the command line version of matcont (cl_matcont). But error dialogue box for “No convergence at x0” was again seen.
(C) I changed my free parameter (I have five parameters and 11 states in total). To my amazement, I was fortunate to see the message “first point found; tangent vector to first point found” in the command window of matlab. I found that I was able to get bifurcation diagrams while selecting either of two parameters as my active parameters (out of five). For the rest of three parameters, when I choose either of these as my active parameters, I get the message “No convergence at x0”. It was further noticed that bifurcation diagrams were computed only for those parameters whose values were very small (almost zero) at the initial equilibrium point. Can some one explain this phenomenon?
(d) The two bifurcation diagrams were not much informative as one was a simple straight vertical line i.e. matcont did not change the value of free parameter and I was getting different values of a particular state for one value of my active parameter. Any comments please?
(e) My 2nd bifurcation diagram was a simple a dot. Does it indicate that no adjacent equilibrium point exists for my initial chosen equilibrium point?
I am using Matcont version 2.5.1 with Matlab 7.0.4 on Windows XP professional version 2002 service pack2.
Your valuable guidance is solicited.
Thanking you in anticipation
Best regards
Qasim
Dear colleagues.
I have started the time integration point from a Bogdanov Takens Point, with the interest of finding the hopf curve. But I again saw the same message "No convergence at x0".
Valuable guidance is desired.
Thanks.
Hi, this is confusing. Time integration is not what you would do for finding a Hopf bifurcation curve. Instead you start continuation Initial point type "BT" and curve type "H(opf)". If that fails, you start slightly away from the BT point, to detect the Hopf point from equilibrium continuation.