I'm new to Matcont. I have a problem with no convergence at x0 after clicking Type-Point and then using the last point in Type-Equilibrium. I try to find out how solution changes depending on the parameter value. I have ODE of 12 equations of periodic functions. I've tried to change initial condition values and Tolerance norms but with no luck. I came back to optimisation using lsqnonlin and I get local minimum possible info, however when playing with Algorithm type and Tolerance values, StepTolerance my ODE still does not converge. I've used the results of that optimisation in the matcont but as I've mentioned with no luck. How can I overcome this problem?
Thank you in advance for any suggestions.
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You mention you have periodic functions in your right hand side, does it mean your system is non-autonomous?
If so, then searching for equilibria is not the way to go. In that case you would consider searching for periodic orbit/limit cycles.
From: Malgo Joan joanna2007@users.sourceforge.net
Sent: Tuesday, January 29, 2019 8:42 PM
To: [matcont:discussion]
Subject: [matcont:discussion] no convergence at x0
Hello,
I'm new to Matcont. I have a problem with no convergence at x0 after clicking Type-Point and then using the last point in Type-Equilibrium. I try to find out how solution changes depending on the parameter value. I have ODE of 12 equations of periodic functions. I've tried to change initial condition values and Tolerance norms but with no luck. I came back to optimisation using lsqnonlin and I get local minimum possible info, however when playing with Algorithm type and Tolerance values, StepTolerance my ODE still does not converge. I've used the results of that optimisation in the matcont but as I've mentioned with no luck. How can I overcome this problem?
Thank you in advance for any suggestions.
Hello hilmeijer,
Thank you for your post. I've got through tutorial for bifurcation for periodic orbit (as you've kindly suggested): Codimension 2 bifurcations of periodic orbits in MatCont using my ODE system. However, I wasn't able to produce bifurcation diagram for chosen parameters. I wonder as in tutorial example was done for SIR model (2 equations) with 2 extra decoupled equations for u and v which I didn't add to my system. Are these equations required for matcont to produce bifurcation? If yes, should they be all added to the removal rate and production rate in my 12 equations?
regards,
On Tuesday 29 January 2019, 20:16:59 GMT, hilmeijer hilmeijer@users.sourceforge.net wrote:
You mention you have periodic functions in your right hand side, does it mean your system is non-autonomous?
If so, then searching for equilibria is not the way to go. In that case you would consider searching for periodic orbit/limit cycles.
From: Malgo Joan joanna2007@users.sourceforge.net
Sent: Tuesday, January 29, 2019 8:42 PM
To: [matcont:discussion]
Subject: [matcont:discussion] no convergence at x0
Hello,
I'm new to Matcont. I have a problem with no convergence at x0 after clicking Type-Point and then using the last point in Type-Equilibrium. I try to find out how solution changes depending on the parameter value. I have ODE of 12 equations of periodic functions. I've tried to change initial condition values and Tolerance norms but with no luck. I came back to optimisation using lsqnonlin and I get local minimum possible info, however when playing with Algorithm type and Tolerance values, StepTolerance my ODE still does not converge. I've used the results of that optimisation in the matcont but as I've mentioned with no luck. How can I overcome this problem?
Thank you in advance for any suggestions.
These two additional equations are required to model the periodic variation with a cosine.
Other than that your post is too cryptic for the forum to help you out. Either state your equations, or say they are autonomous, but give more details.
Best, Hil
From: Malgo Joan joanna2007@users.sourceforge.net
Sent: Wednesday, January 30, 2019 10:30 AM
To: [matcont:discussion]
Subject: [matcont:discussion] Re: no convergence at x0
Hello hilmeijer,
Thank you for your post. I've got through tutorial for bifurcation for periodic orbit (as you've kindly suggested): Codimension 2 bifurcations of periodic orbits in MatCont using my ODE system. However, I wasn't able to produce bifurcation diagram for chosen parameters. I wonder as in tutorial example was done for SIR model (2 equations) with 2 extra decoupled equations for u and v which I didn't add to my system. Are these equations required for matcont to produce bifurcation? If yes, should they be all added to the removal rate and production rate in my 12 equations?
regards,
On Tuesday 29 January 2019, 20:16:59 GMT, hilmeijer hilmeijer@users.sourceforge.net wrote:
You mention you have periodic functions in your right hand side, does it mean your system is non-autonomous?
If so, then searching for equilibria is not the way to go. In that case you would consider searching for periodic orbit/limit cycles.
From: Malgo Joan joanna2007@users.sourceforge.net
Sent: Tuesday, January 29, 2019 8:42 PM
To: [matcont:discussion]
Subject: [matcont:discussion] no convergence at x0
Hello,
I'm new to Matcont. I have a problem with no convergence at x0 after clicking Type-Point and then using the last point in Type-Equilibrium. I try to find out how solution changes depending on the parameter value. I have ODE of 12 equations of periodic functions. I've tried to change initial condition values and Tolerance norms but with no luck. I came back to optimisation using lsqnonlin and I get local minimum possible info, however when playing with Algorithm type and Tolerance values, StepTolerance my ODE still does not converge. I've used the results of that optimisation in the matcont but as I've mentioned with no luck. How can I overcome this problem?
Thank you in advance for any suggestions.
Hello Hil,
Thank you for your reply. I didn't check my private e-mail for a while and I've missed your reply.My ODE system is similar to the following ODE of 12 differential equations and contains 1 algebraic equation:
L=2(18.311G^5-59.062G^4+68.983G^3-34.283G^2+5.9711G+0.6839);
I'll be very grateful if you would be able to give me a hint how I should build in the periodic variation with cosine. Should I calculate periodic function using sin and cos to do it? But, then how should I feed into ODE?
Thanks for Your help,
regards,Malgo
On Tuesday 5 February 2019, 16:29:55 GMT, hilmeijer <hilmeijer@users.sourceforge.net> wrote:
Dear Malgo,
These two additional equations are required to model the periodic variation with a cosine.
Other than that your post is too cryptic for the forum to help you out. Either state your equations, or say they are autonomous, but give more details.
Best, Hil
From: Malgo Joan joanna2007@users.sourceforge.net
Sent: Wednesday, January 30, 2019 10:30 AM
To: [matcont:discussion]
Subject: [matcont:discussion] Re: no convergence at x0
Hello hilmeijer,
Thank you for your post. I've got through tutorial for bifurcation for periodic orbit (as you've kindly suggested): Codimension 2 bifurcations of periodic orbits in MatCont using my ODE system. However, I wasn't able to produce bifurcation diagram for chosen parameters. I wonder as in tutorial example was done for SIR model (2 equations) with 2 extra decoupled equations for u and v which I didn't add to my system. Are these equations required for matcont to produce bifurcation? If yes, should they be all added to the removal rate and production rate in my 12 equations?
regards,
On Tuesday 29 January 2019, 20:16:59 GMT, hilmeijer hilmeijer@users.sourceforge.net wrote:
You mention you have periodic functions in your right hand side, does it mean your system is non-autonomous?
If so, then searching for equilibria is not the way to go. In that case you would consider searching for periodic orbit/limit cycles.
From: Malgo Joan joanna2007@users.sourceforge.net
Sent: Tuesday, January 29, 2019 8:42 PM
To: [matcont:discussion]
Subject: [matcont:discussion] no convergence at x0
Hello,
I'm new to Matcont. I have a problem with no convergence at x0 after clicking Type-Point and then using the last point in Type-Equilibrium. I try to find out how solution changes depending on the parameter value. I have ODE of 12 equations of periodic functions. I've tried to change initial condition values and Tolerance norms but with no luck. I came back to optimisation using lsqnonlin and I get local minimum possible info, however when playing with Algorithm type and Tolerance values, StepTolerance my ODE still does not converge. I've used the results of that optimisation in the matcont but as I've mentioned with no luck. How can I overcome this problem?
Thank you in advance for any suggestions.
This is the Hopf-normal form with solution u=cos(w*t+phi), and phi corresponds to the initial condition.
Now start with nonzero u,v, e.g. u=1,v=0, and then you can use u as periodic variable for your other 12 variables.
From: Malgo Joan joanna2007@users.sourceforge.net
Sent: Saturday, February 16, 2019 1:31 PM
To: [matcont:discussion]
Subject: [matcont:discussion] Re: no convergence at x0
Hello Hil,
Thank you for your reply. I didn't check my private e-mail for a while and I've missed your reply.My ODE system is similar to the following ODE of 12 differential equations and contains 1 algebraic equation:
L=2(18.311G^5-59.062G^4+68.983G^3-34.283G^2+5.9711G+0.6839);
I'll be very grateful if you would be able to give me a hint how I should build in the periodic variation with cosine. Should I calculate periodic function using sin and cos to do it? But, then how should I feed into ODE?
Thanks for Your help,
regards,Malgo
On Tuesday 5 February 2019, 16:29:55 GMT, hilmeijer <hilmeijer@users.sourceforge.net> wrote:
Dear Malgo,
These two additional equations are required to model the periodic variation with a cosine.
Other than that your post is too cryptic for the forum to help you out. Either state your equations, or say they are autonomous, but give more details.
Best, Hil
From: Malgo Joan joanna2007@users.sourceforge.net
Sent: Wednesday, January 30, 2019 10:30 AM
To: [matcont:discussion]
Subject: [matcont:discussion] Re: no convergence at x0
Hello hilmeijer,
Thank you for your post. I've got through tutorial for bifurcation for periodic orbit (as you've kindly suggested): Codimension 2 bifurcations of periodic orbits in MatCont using my ODE system. However, I wasn't able to produce bifurcation diagram for chosen parameters. I wonder as in tutorial example was done for SIR model (2 equations) with 2 extra decoupled equations for u and v which I didn't add to my system. Are these equations required for matcont to produce bifurcation? If yes, should they be all added to the removal rate and production rate in my 12 equations?
regards,
On Tuesday 29 January 2019, 20:16:59 GMT, hilmeijer hilmeijer@users.sourceforge.net wrote:
You mention you have periodic functions in your right hand side, does it mean your system is non-autonomous?
If so, then searching for equilibria is not the way to go. In that case you would consider searching for periodic orbit/limit cycles.
From: Malgo Joan joanna2007@users.sourceforge.net
Sent: Tuesday, January 29, 2019 8:42 PM
To: [matcont:discussion]
Subject: [matcont:discussion] no convergence at x0
Hello,
I'm new to Matcont. I have a problem with no convergence at x0 after clicking Type-Point and then using the last point in Type-Equilibrium. I try to find out how solution changes depending on the parameter value. I have ODE of 12 equations of periodic functions. I've tried to change initial condition values and Tolerance norms but with no luck. I came back to optimisation using lsqnonlin and I get local minimum possible info, however when playing with Algorithm type and Tolerance values, StepTolerance my ODE still does not converge. I've used the results of that optimisation in the matcont but as I've mentioned with no luck. How can I overcome this problem?
Thank you in advance for any suggestions.
Hello Hil,
Thank you very much. Your guidance was the most useful. I know how to do it now. Thank you very much once again.
Malgo
On Tuesday 19 February 2019, 14:36:32 GMT, hilmeijer hilmeijer@users.sourceforge.net wrote:
You add two additional equations
u'=-wv+u(1-u^2-v^2)
v'=wu+v(1-u^2-v^2)
This is the Hopf-normal form with solution u=cos(w*t+phi), and phi corresponds to the initial condition.
Now start with nonzero u,v, e.g. u=1,v=0, and then you can use u as periodic variable for your other 12 variables.
From: Malgo Joan joanna2007@users.sourceforge.net
Sent: Saturday, February 16, 2019 1:31 PM
To: [matcont:discussion]
Subject: [matcont:discussion] Re: no convergence at x0
Hello Hil,
Thank you for your reply. I didn't check my private e-mail for a while and I've missed your reply.My ODE system is similar to the following ODE of 12 differential equations and contains 1 algebraic equation:
L=2(18.311G^5-59.062G^4+68.983G^3-34.283G^2+5.9711G+0.6839);
I'll be very grateful if you would be able to give me a hint how I should build in the periodic variation with cosine. Should I calculate periodic function using sin and cos to do it? But, then how should I feed into ODE?
Thanks for Your help,
regards,Malgo
On Tuesday 5 February 2019, 16:29:55 GMT, hilmeijer hilmeijer@users.sourceforge.net wrote:
Dear Malgo,
These two additional equations are required to model the periodic variation with a cosine.
Other than that your post is too cryptic for the forum to help you out. Either state your equations, or say they are autonomous, but give more details.
Best, Hil
From: Malgo Joan joanna2007@users.sourceforge.net
Sent: Wednesday, January 30, 2019 10:30 AM
To: [matcont:discussion]
Subject: [matcont:discussion] Re: no convergence at x0
Hello hilmeijer,
Thank you for your post. I've got through tutorial for bifurcation for periodic orbit (as you've kindly suggested): Codimension 2 bifurcations of periodic orbits in MatCont using my ODE system. However, I wasn't able to produce bifurcation diagram for chosen parameters. I wonder as in tutorial example was done for SIR model (2 equations) with 2 extra decoupled equations for u and v which I didn't add to my system. Are these equations required for matcont to produce bifurcation? If yes, should they be all added to the removal rate and production rate in my 12 equations?
regards,
On Tuesday 29 January 2019, 20:16:59 GMT, hilmeijer hilmeijer@users.sourceforge.net wrote:
You mention you have periodic functions in your right hand side, does it mean your system is non-autonomous?
If so, then searching for equilibria is not the way to go. In that case you would consider searching for periodic orbit/limit cycles.
From: Malgo Joan joanna2007@users.sourceforge.net
Sent: Tuesday, January 29, 2019 8:42 PM
To: [matcont:discussion]
Subject: [matcont:discussion] no convergence at x0
Hello,
I'm new to Matcont. I have a problem with no convergence at x0 after clicking Type-Point and then using the last point in Type-Equilibrium. I try to find out how solution changes depending on the parameter value. I have ODE of 12 equations of periodic functions. I've tried to change initial condition values and Tolerance norms but with no luck. I came back to optimisation using lsqnonlin and I get local minimum possible info, however when playing with Algorithm type and Tolerance values, StepTolerance my ODE still does not converge. I've used the results of that optimisation in the matcont but as I've mentioned with no luck. How can I overcome this problem?
Thank you in advance for any suggestions.
Hello,
I'm new to Matcont. I have a problem with no convergence at x0 after clicking Type-Point and then using the last point in Type-Equilibrium. I try to find out how solution changes depending on the parameter value. I have ODE of 12 equations of periodic functions. I've tried to change initial condition values and Tolerance norms but with no luck. I came back to optimisation using lsqnonlin and I get local minimum possible info, however when playing with Algorithm type and Tolerance values, StepTolerance my ODE still does not converge. I've used the results of that optimisation in the matcont but as I've mentioned with no luck. How can I overcome this problem?
Thank you in advance for any suggestions.
You mention you have periodic functions in your right hand side, does it mean your system is non-autonomous?
If so, then searching for equilibria is not the way to go. In that case you would consider searching for periodic orbit/limit cycles.
From: Malgo Joan joanna2007@users.sourceforge.net
Sent: Tuesday, January 29, 2019 8:42 PM
To: [matcont:discussion]
Subject: [matcont:discussion] no convergence at x0
Hello,
I'm new to Matcont. I have a problem with no convergence at x0 after clicking Type-Point and then using the last point in Type-Equilibrium. I try to find out how solution changes depending on the parameter value. I have ODE of 12 equations of periodic functions. I've tried to change initial condition values and Tolerance norms but with no luck. I came back to optimisation using lsqnonlin and I get local minimum possible info, however when playing with Algorithm type and Tolerance values, StepTolerance my ODE still does not converge. I've used the results of that optimisation in the matcont but as I've mentioned with no luck. How can I overcome this problem?
Thank you in advance for any suggestions.
no convergence at x0
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/
Hello hilmeijer,
Thank you for your post. I've got through tutorial for bifurcation for periodic orbit (as you've kindly suggested): Codimension 2 bifurcations of periodic orbits in MatCont using my ODE system. However, I wasn't able to produce bifurcation diagram for chosen parameters. I wonder as in tutorial example was done for SIR model (2 equations) with 2 extra decoupled equations for u and v which I didn't add to my system. Are these equations required for matcont to produce bifurcation? If yes, should they be all added to the removal rate and production rate in my 12 equations?
regards,
On Tuesday 29 January 2019, 20:16:59 GMT, hilmeijer hilmeijer@users.sourceforge.net wrote:
You mention you have periodic functions in your right hand side, does it mean your system is non-autonomous?
If so, then searching for equilibria is not the way to go. In that case you would consider searching for periodic orbit/limit cycles.
From: Malgo Joan joanna2007@users.sourceforge.net
Sent: Tuesday, January 29, 2019 8:42 PM
To: [matcont:discussion]
Subject: [matcont:discussion] no convergence at x0
Hello,
I'm new to Matcont. I have a problem with no convergence at x0 after clicking Type-Point and then using the last point in Type-Equilibrium. I try to find out how solution changes depending on the parameter value. I have ODE of 12 equations of periodic functions. I've tried to change initial condition values and Tolerance norms but with no luck. I came back to optimisation using lsqnonlin and I get local minimum possible info, however when playing with Algorithm type and Tolerance values, StepTolerance my ODE still does not converge. I've used the results of that optimisation in the matcont but as I've mentioned with no luck. How can I overcome this problem?
Thank you in advance for any suggestions.
no convergence at x0
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/
no convergence at x0
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/
Dear Malgo,
These two additional equations are required to model the periodic variation with a cosine.
Other than that your post is too cryptic for the forum to help you out. Either state your equations, or say they are autonomous, but give more details.
Best, Hil
From: Malgo Joan joanna2007@users.sourceforge.net
Sent: Wednesday, January 30, 2019 10:30 AM
To: [matcont:discussion]
Subject: [matcont:discussion] Re: no convergence at x0
Hello hilmeijer,
Thank you for your post. I've got through tutorial for bifurcation for periodic orbit (as you've kindly suggested): Codimension 2 bifurcations of periodic orbits in MatCont using my ODE system. However, I wasn't able to produce bifurcation diagram for chosen parameters. I wonder as in tutorial example was done for SIR model (2 equations) with 2 extra decoupled equations for u and v which I didn't add to my system. Are these equations required for matcont to produce bifurcation? If yes, should they be all added to the removal rate and production rate in my 12 equations?
regards,
On Tuesday 29 January 2019, 20:16:59 GMT, hilmeijer hilmeijer@users.sourceforge.net wrote:
You mention you have periodic functions in your right hand side, does it mean your system is non-autonomous?
If so, then searching for equilibria is not the way to go. In that case you would consider searching for periodic orbit/limit cycles.
From: Malgo Joan joanna2007@users.sourceforge.net
Sent: Tuesday, January 29, 2019 8:42 PM
To: [matcont:discussion]
Subject: [matcont:discussion] no convergence at x0
Hello,
I'm new to Matcont. I have a problem with no convergence at x0 after clicking Type-Point and then using the last point in Type-Equilibrium. I try to find out how solution changes depending on the parameter value. I have ODE of 12 equations of periodic functions. I've tried to change initial condition values and Tolerance norms but with no luck. I came back to optimisation using lsqnonlin and I get local minimum possible info, however when playing with Algorithm type and Tolerance values, StepTolerance my ODE still does not converge. I've used the results of that optimisation in the matcont but as I've mentioned with no luck. How can I overcome this problem?
Thank you in advance for any suggestions.
no convergence at x0
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/
no convergence at x0
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/
no convergence at x0
Sent from sourceforge.net because you indicated interest in https://sourceforge.net/p/matcont/discussion/762214/
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Hello Hil,
Thank you for your reply. I didn't check my private e-mail for a while and I've missed your reply.My ODE system is similar to the following ODE of 12 differential equations and contains 1 algebraic equation:
L=2(18.311G^5-59.062G^4+68.983G^3-34.283G^2+5.9711G+0.6839);
dxdt(1)=k_A(1/(1+(B/T_A_B)^n_A_B))-alpha_AA
dxdt(2)=k_B((G/T_B_G)^n_B_G/(1+(G/T_B_G)^n_B_G))(1/(1+(D/T_B^D)^n_B_D))-alpha_B*B
dxdt(3)=k_C((E/T_C_E)^n_C_E/(1+(E/T_C_E)^n_C_E))((D/T_C^D)^n_C_D/(1+(D/T_C^D)^n_C_D))+k_C_B(1/(1+(B/T_C^B)^n_C_B))-alpha_CC
dxdt(4)=c_D_Foll1(Foll((L/k)^n/(1+(L/k)^n)))^2-c_D1*D
dxdt(5)=c_E_Foll1(Foll)^2-c_E1E
dxdt(6)=m_Foll_CC^3/((T_Foll_CT_C^2/(T_C_Foll^2+Foll^2))^2+C^3)-...
[m_Foll_GG^5/(T_Foll_G^5+G^5)+m_Ovul_Foll_A(A^3/(T_Ovul_Foll_A^2+A^3))]*Foll;
dxdt(7)=SFm_Ovul_Foll_A(A^2/(T_Ovul_Foll_A^2+A^2))Foll+m_F_FF^2/(T_F_F^2+F^2)-...
m_F_J(J^5/(T_F_J^5+J^5))F;
dxdt(8)=cPFaF^2-alpha_PG;
dxdt(9)=m_H_GG^5/(T_H_G^5+G^5)-c_HH;
dxdt(10)=m_I_D(D^2/(T_I_D^2+D^2))F^2-c_I*I;
dxdt(11)=m_J_K_F(K^5/(T_J_K^5+K^5))(F^10/(T_J_F^10+F^10))-c_J*J;
dxdt(12)=m_K_H_I(H^5/(T_K_H^5+H^5))(I^2/(T_K_I^2+I^2))-c_K*K;
I'll be very grateful if you would be able to give me a hint how I should build in the periodic variation with cosine. Should I calculate periodic function using sin and cos to do it? But, then how should I feed into ODE?
Thanks for Your help,
regards,Malgo
Dear Malgo,
These two additional equations are required to model the periodic variation with a cosine.
Other than that your post is too cryptic for the forum to help you out. Either state your equations, or say they are autonomous, but give more details.
Best, Hil
From: Malgo Joan joanna2007@users.sourceforge.net
Sent: Wednesday, January 30, 2019 10:30 AM
To: [matcont:discussion]
Subject: [matcont:discussion] Re: no convergence at x0
Hello hilmeijer,
Thank you for your post. I've got through tutorial for bifurcation for periodic orbit (as you've kindly suggested): Codimension 2 bifurcations of periodic orbits in MatCont using my ODE system. However, I wasn't able to produce bifurcation diagram for chosen parameters. I wonder as in tutorial example was done for SIR model (2 equations) with 2 extra decoupled equations for u and v which I didn't add to my system. Are these equations required for matcont to produce bifurcation? If yes, should they be all added to the removal rate and production rate in my 12 equations?
regards,
On Tuesday 29 January 2019, 20:16:59 GMT, hilmeijer hilmeijer@users.sourceforge.net wrote:
You mention you have periodic functions in your right hand side, does it mean your system is non-autonomous?
If so, then searching for equilibria is not the way to go. In that case you would consider searching for periodic orbit/limit cycles.
From: Malgo Joan joanna2007@users.sourceforge.net
Sent: Tuesday, January 29, 2019 8:42 PM
To: [matcont:discussion]
Subject: [matcont:discussion] no convergence at x0
Hello,
I'm new to Matcont. I have a problem with no convergence at x0 after clicking Type-Point and then using the last point in Type-Equilibrium. I try to find out how solution changes depending on the parameter value. I have ODE of 12 equations of periodic functions. I've tried to change initial condition values and Tolerance norms but with no luck. I came back to optimisation using lsqnonlin and I get local minimum possible info, however when playing with Algorithm type and Tolerance values, StepTolerance my ODE still does not converge. I've used the results of that optimisation in the matcont but as I've mentioned with no luck. How can I overcome this problem?
Thank you in advance for any suggestions.
no convergence at x0
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/
no convergence at x0
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/
no convergence at x0
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no convergence at x0
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You add two additional equations
u'=-wv+u(1-u^2-v^2)
v'=wu+v(1-u^2-v^2)
This is the Hopf-normal form with solution u=cos(w*t+phi), and phi corresponds to the initial condition.
Now start with nonzero u,v, e.g. u=1,v=0, and then you can use u as periodic variable for your other 12 variables.
From: Malgo Joan joanna2007@users.sourceforge.net
Sent: Saturday, February 16, 2019 1:31 PM
To: [matcont:discussion]
Subject: [matcont:discussion] Re: no convergence at x0
Hello Hil,
Thank you for your reply. I didn't check my private e-mail for a while and I've missed your reply.My ODE system is similar to the following ODE of 12 differential equations and contains 1 algebraic equation:
L=2(18.311G^5-59.062G^4+68.983G^3-34.283G^2+5.9711G+0.6839);
dxdt(1)=k_A(1/(1+(B/T_A_B)^n_A_B))-alpha_AA
dxdt(2)=k_B((G/T_B_G)^n_B_G/(1+(G/T_B_G)^n_B_G))(1/(1+(D/T_B^D)^n_B_D))-alpha_B*B
dxdt(3)=k_C((E/T_C_E)^n_C_E/(1+(E/T_C_E)^n_C_E))((D/T_C^D)^n_C_D/(1+(D/T_C^D)^n_C_D))+k_C_B(1/(1+(B/T_C^B)^n_C_B))-alpha_CC
dxdt(4)=c_D_Foll1(Foll((L/k)^n/(1+(L/k)^n)))^2-c_D1*D
dxdt(5)=c_E_Foll1(Foll)^2-c_E1E
dxdt(6)=m_Foll_CC^3/((T_Foll_CT_C^2/(T_C_Foll^2+Foll^2))^2+C^3)-...
dxdt(7)=SFm_Ovul_Foll_A(A^2/(T_Ovul_Foll_A^2+A^2))Foll+m_F_FF^2/(T_F_F^2+F^2)-...
dxdt(8)=cPFaF^2-alpha_PG;
dxdt(9)=m_H_GG^5/(T_H_G^5+G^5)-c_HH;
dxdt(10)=m_I_D(D^2/(T_I_D^2+D^2))F^2-c_I*I;
dxdt(11)=m_J_K_F(K^5/(T_J_K^5+K^5))(F^10/(T_J_F^10+F^10))-c_J*J;
dxdt(12)=m_K_H_I(H^5/(T_K_H^5+H^5))(I^2/(T_K_I^2+I^2))-c_K*K;
I'll be very grateful if you would be able to give me a hint how I should build in the periodic variation with cosine. Should I calculate periodic function using sin and cos to do it? But, then how should I feed into ODE?
Thanks for Your help,
regards,Malgo
Dear Malgo,
These two additional equations are required to model the periodic variation with a cosine.
Other than that your post is too cryptic for the forum to help you out. Either state your equations, or say they are autonomous, but give more details.
Best, Hil
From: Malgo Joan joanna2007@users.sourceforge.net
Sent: Wednesday, January 30, 2019 10:30 AM
To: [matcont:discussion]
Subject: [matcont:discussion] Re: no convergence at x0
Hello hilmeijer,
Thank you for your post. I've got through tutorial for bifurcation for periodic orbit (as you've kindly suggested): Codimension 2 bifurcations of periodic orbits in MatCont using my ODE system. However, I wasn't able to produce bifurcation diagram for chosen parameters. I wonder as in tutorial example was done for SIR model (2 equations) with 2 extra decoupled equations for u and v which I didn't add to my system. Are these equations required for matcont to produce bifurcation? If yes, should they be all added to the removal rate and production rate in my 12 equations?
regards,
On Tuesday 29 January 2019, 20:16:59 GMT, hilmeijer hilmeijer@users.sourceforge.net wrote:
You mention you have periodic functions in your right hand side, does it mean your system is non-autonomous?
If so, then searching for equilibria is not the way to go. In that case you would consider searching for periodic orbit/limit cycles.
From: Malgo Joan joanna2007@users.sourceforge.net
Sent: Tuesday, January 29, 2019 8:42 PM
To: [matcont:discussion]
Subject: [matcont:discussion] no convergence at x0
Hello,
I'm new to Matcont. I have a problem with no convergence at x0 after clicking Type-Point and then using the last point in Type-Equilibrium. I try to find out how solution changes depending on the parameter value. I have ODE of 12 equations of periodic functions. I've tried to change initial condition values and Tolerance norms but with no luck. I came back to optimisation using lsqnonlin and I get local minimum possible info, however when playing with Algorithm type and Tolerance values, StepTolerance my ODE still does not converge. I've used the results of that optimisation in the matcont but as I've mentioned with no luck. How can I overcome this problem?
Thank you in advance for any suggestions.
no convergence at x0
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no convergence at x0
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Hello Hil,
Thank you very much. Your guidance was the most useful. I know how to do it now. Thank you very much once again.
Malgo
On Tuesday 19 February 2019, 14:36:32 GMT, hilmeijer hilmeijer@users.sourceforge.net wrote:
You add two additional equations
u'=-wv+u(1-u^2-v^2)
v'=wu+v(1-u^2-v^2)
This is the Hopf-normal form with solution u=cos(w*t+phi), and phi corresponds to the initial condition.
Now start with nonzero u,v, e.g. u=1,v=0, and then you can use u as periodic variable for your other 12 variables.
From: Malgo Joan joanna2007@users.sourceforge.net
Sent: Saturday, February 16, 2019 1:31 PM
To: [matcont:discussion]
Subject: [matcont:discussion] Re: no convergence at x0
Hello Hil,
Thank you for your reply. I didn't check my private e-mail for a while and I've missed your reply.My ODE system is similar to the following ODE of 12 differential equations and contains 1 algebraic equation:
L=2(18.311G^5-59.062G^4+68.983G^3-34.283G^2+5.9711G+0.6839);
dxdt(1)=k_A(1/(1+(B/T_A_B)^n_A_B))-alpha_AA
dxdt(2)=k_B((G/T_B_G)^n_B_G/(1+(G/T_B_G)^n_B_G))(1/(1+(D/T_B^D)^n_B_D))-alpha_B*B
dxdt(3)=k_C((E/T_C_E)^n_C_E/(1+(E/T_C_E)^n_C_E))((D/T_C^D)^n_C_D/(1+(D/T_C^D)^n_C_D))+k_C_B(1/(1+(B/T_C^B)^n_C_B))-alpha_CC
dxdt(4)=c_D_Foll1(Foll((L/k)^n/(1+(L/k)^n)))^2-c_D1*D
dxdt(5)=c_E_Foll1(Foll)^2-c_E1E
dxdt(6)=m_Foll_CC^3/((T_Foll_CT_C^2/(T_C_Foll^2+Foll^2))^2+C^3)-...
[m_Foll_GG^5/(T_Foll_G^5+G^5)+m_Ovul_Foll_A(A^3/(T_Ovul_Foll_A^2+A^3))]*Foll;
dxdt(7)=SFm_Ovul_Foll_A(A^2/(T_Ovul_Foll_A^2+A^2))Foll+m_F_FF^2/(T_F_F^2+F^2)-...
m_F_J(J^5/(T_F_J^5+J^5))F;
dxdt(8)=cPFaF^2-alpha_PG;
dxdt(9)=m_H_GG^5/(T_H_G^5+G^5)-c_HH;
dxdt(10)=m_I_D(D^2/(T_I_D^2+D^2))F^2-c_I*I;
dxdt(11)=m_J_K_F(K^5/(T_J_K^5+K^5))(F^10/(T_J_F^10+F^10))-c_J*J;
dxdt(12)=m_K_H_I(H^5/(T_K_H^5+H^5))(I^2/(T_K_I^2+I^2))-c_K*K;
I'll be very grateful if you would be able to give me a hint how I should build in the periodic variation with cosine. Should I calculate periodic function using sin and cos to do it? But, then how should I feed into ODE?
Thanks for Your help,
regards,Malgo
On Tuesday 5 February 2019, 16:29:55 GMT, hilmeijer hilmeijer@users.sourceforge.net wrote:
Dear Malgo,
These two additional equations are required to model the periodic variation with a cosine.
Other than that your post is too cryptic for the forum to help you out. Either state your equations, or say they are autonomous, but give more details.
Best, Hil
From: Malgo Joan joanna2007@users.sourceforge.net
Sent: Wednesday, January 30, 2019 10:30 AM
To: [matcont:discussion]
Subject: [matcont:discussion] Re: no convergence at x0
Hello hilmeijer,
Thank you for your post. I've got through tutorial for bifurcation for periodic orbit (as you've kindly suggested): Codimension 2 bifurcations of periodic orbits in MatCont using my ODE system. However, I wasn't able to produce bifurcation diagram for chosen parameters. I wonder as in tutorial example was done for SIR model (2 equations) with 2 extra decoupled equations for u and v which I didn't add to my system. Are these equations required for matcont to produce bifurcation? If yes, should they be all added to the removal rate and production rate in my 12 equations?
regards,
On Tuesday 29 January 2019, 20:16:59 GMT, hilmeijer hilmeijer@users.sourceforge.net wrote:
You mention you have periodic functions in your right hand side, does it mean your system is non-autonomous?
If so, then searching for equilibria is not the way to go. In that case you would consider searching for periodic orbit/limit cycles.
From: Malgo Joan joanna2007@users.sourceforge.net
Sent: Tuesday, January 29, 2019 8:42 PM
To: [matcont:discussion]
Subject: [matcont:discussion] no convergence at x0
Hello,
I'm new to Matcont. I have a problem with no convergence at x0 after clicking Type-Point and then using the last point in Type-Equilibrium. I try to find out how solution changes depending on the parameter value. I have ODE of 12 equations of periodic functions. I've tried to change initial condition values and Tolerance norms but with no luck. I came back to optimisation using lsqnonlin and I get local minimum possible info, however when playing with Algorithm type and Tolerance values, StepTolerance my ODE still does not converge. I've used the results of that optimisation in the matcont but as I've mentioned with no luck. How can I overcome this problem?
Thank you in advance for any suggestions.
no convergence at x0
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no convergence at x0
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no convergence at x0
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no convergence at x0
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no convergence at x0
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no convergence at x0
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