MATCONT detected several period doubling bifurcations for my system of equations. However, all of them have extremely small normal form coefficients (of the order of 10^-10 and 10^-9). Are these reliable? What is the implication of having such small normal form coefficients?
Thanks and Regards,
Parul
If you would like to refer to this comment somewhere else in this project, copy and paste the following link:
Such things depend a lot on the details of the system. Is it stiff or not, and so on. They all influence settings you need for accurate results.
Being small is not necessarily bad, you could try to pick a PD point and continue a Period-doubling curve in two parameters. If the normal form coefficient along that curve behaves erratic then you need to look into settings to increase accuracy.
Best, Hil
From: Parul Verma parulv1@users.sourceforge.net
Sent: Friday, April 19, 2019 6:07 PM
To: [matcont:discussion]
Subject: [matcont:discussion] Period doubling bifurcations with small normal form coefficients
Hello,
MATCONT detected several period doubling bifurcations for my system of equations. However, all of them have extremely small normal form coefficients (of the order of 10^-10 and 10^-9). Are these reliable? What is the implication of having such small normal form coefficients?
Thank you for your help. I am working on Hodgkin-Huxley type equations. It is stiff. I tried 2 parameter continuation from various PD points and observed a similar pattern. The system would detect lot of generalized period doubling points, but with a warning that the cubic coefficient of the normal form is not zero. Also, the computations take lot of time when I do 2 parameter continuation from a PD point.
I will increase the accuracy and try the continuations again.
Thank you,
Parul
If you would like to refer to this comment somewhere else in this project, copy and paste the following link:
I increased ntst from 100 to 500 and found a PD point for which the normal form coefficient increased from approx. 10^-10 to 10^-7. Does this mean that there is definitely a PD point?
Secondly, I tried 2 parameter continuation from this PD point and did not see any warnings about cubic coefficients this time. Matcont did not detect any codimension-2 bifurcation this time, although it was detecting a generalized period doubling bifurcation earlier.
You also mentioned that I should check how the normal form coefficients behave while doing the 2 parameter continuation. How to do that? I don't see any option of checking the normal form coefficients in this case. I am using the command line version of Matcont.
Thanks and Regards,
Parul
If you would like to refer to this comment somewhere else in this project, copy and paste the following link:
sorry for the delay in the reply, your email got lost somehow.
very likely, see below.
If you monitor the (Floquet) multipliers, then there must be crossing -1 at the bifurcation, that certainly is proper evidence.
Multipliers you find in the f-variable. (referring to CL-usage [x,v,h,s,f]=cont...)
Along a PD-curve you can test for a degenerate PD. This test function is the normal form coefficient and is stored in h. So if that is a smooth curve, then yes, you can trust it, even if it small.
From: Parul Verma parulv1@users.sourceforge.net
Sent: Friday, April 26, 2019 10:38:19 PM
To: [matcont:discussion]
Subject: [matcont:discussion] Period doubling bifurcations with small normal form coefficients
Dear Hil,
I increased ntst from 100 to 500 and found a PD point for which the normal form coefficient increased from approx. 10^-10 to 10^-7. Does this mean that there is definitely a PD point?
Secondly, I tried 2 parameter continuation from this PD point and did not see any warnings about cubic coefficients this time. Matcont did not detect any codimension-2 bifurcation this time, although it was detecting a generalized period doubling bifurcation earlier.
You also mentioned that I should check how the normal form coefficients behave while doing the 2 parameter continuation. How to do that? I don't see any option of checking the normal form coefficients in this case. I am using the command line version of Matcont.
I looked at the f-variable and I don't understand them. My system of ODEs have 9 variables, and I performed continuation for 50 steps. So, I assume that f should be of dimension 9 X 50. However, f was of dimension 110 X 50. Why is that so?
Regards,
Parul
If you would like to refer to this comment somewhere else in this project, copy and paste the following link:
The first 101 numbers correspond to the timepoints of the time-discretization.
You need numbers 102-110 for the multipliers
From: Parul Verma parulv1@users.sourceforge.net
Sent: Thursday, May 16, 2019 8:22 PM
To: [matcont:discussion]
Subject: [matcont:discussion] Period doubling bifurcations with small normal form coefficients
Dear Hil,
I looked at the f-variable and I don't understand them. My system of ODEs have 9 variables, and I performed continuation for 50 steps. So, I assume that f should be of dimension 9 X 50. However, f was of dimension 110 X 50. Why is that so?
Hello,
MATCONT detected several period doubling bifurcations for my system of equations. However, all of them have extremely small normal form coefficients (of the order of 10^-10 and 10^-9). Are these reliable? What is the implication of having such small normal form coefficients?
Thanks and Regards,
Parul
Dear Parul,
Such things depend a lot on the details of the system. Is it stiff or not, and so on. They all influence settings you need for accurate results.
Being small is not necessarily bad, you could try to pick a PD point and continue a Period-doubling curve in two parameters. If the normal form coefficient along that curve behaves erratic then you need to look into settings to increase accuracy.
Best, Hil
From: Parul Verma parulv1@users.sourceforge.net
Sent: Friday, April 19, 2019 6:07 PM
To: [matcont:discussion]
Subject: [matcont:discussion] Period doubling bifurcations with small normal form coefficients
Hello,
MATCONT detected several period doubling bifurcations for my system of equations. However, all of them have extremely small normal form coefficients (of the order of 10^-10 and 10^-9). Are these reliable? What is the implication of having such small normal form coefficients?
Thanks and Regards,
Parul
Period doubling bifurcations with small normal form coefficients
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 Hil,
Thank you for your help. I am working on Hodgkin-Huxley type equations. It is stiff. I tried 2 parameter continuation from various PD points and observed a similar pattern. The system would detect lot of generalized period doubling points, but with a warning that the cubic coefficient of the normal form is not zero. Also, the computations take lot of time when I do 2 parameter continuation from a PD point.
I will increase the accuracy and try the continuations again.
Thank you,
Parul
In particular increase the number of mesh points ntst, but keep ncol=4
Dear Hil,
I increased ntst from 100 to 500 and found a PD point for which the normal form coefficient increased from approx. 10^-10 to 10^-7. Does this mean that there is definitely a PD point?
Secondly, I tried 2 parameter continuation from this PD point and did not see any warnings about cubic coefficients this time. Matcont did not detect any codimension-2 bifurcation this time, although it was detecting a generalized period doubling bifurcation earlier.
You also mentioned that I should check how the normal form coefficients behave while doing the 2 parameter continuation. How to do that? I don't see any option of checking the normal form coefficients in this case. I am using the command line version of Matcont.
Thanks and Regards,
Parul
From: Parul Verma parulv1@users.sourceforge.net
Sent: Friday, April 26, 2019 10:38:19 PM
To: [matcont:discussion]
Subject: [matcont:discussion] Period doubling bifurcations with small normal form coefficients
Dear Hil,
I increased ntst from 100 to 500 and found a PD point for which the normal form coefficient increased from approx. 10^-10 to 10^-7. Does this mean that there is definitely a PD point?
Secondly, I tried 2 parameter continuation from this PD point and did not see any warnings about cubic coefficients this time. Matcont did not detect any codimension-2 bifurcation this time, although it was detecting a generalized period doubling bifurcation earlier.
You also mentioned that I should check how the normal form coefficients behave while doing the 2 parameter continuation. How to do that? I don't see any option of checking the normal form coefficients in this case. I am using the command line version of Matcont.
Thanks and Regards,
Parul
Period doubling bifurcations with small normal form coefficients
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 Hil,
I looked at the f-variable and I don't understand them. My system of ODEs have 9 variables, and I performed continuation for 50 steps. So, I assume that f should be of dimension 9 X 50. However, f was of dimension 110 X 50. Why is that so?
Regards,
Parul
The first 101 numbers correspond to the timepoints of the time-discretization.
You need numbers 102-110 for the multipliers
From: Parul Verma parulv1@users.sourceforge.net
Sent: Thursday, May 16, 2019 8:22 PM
To: [matcont:discussion]
Subject: [matcont:discussion] Period doubling bifurcations with small normal form coefficients
Dear Hil,
I looked at the f-variable and I don't understand them. My system of ODEs have 9 variables, and I performed continuation for 50 steps. So, I assume that f should be of dimension 9 X 50. However, f was of dimension 110 X 50. Why is that so?
Regards,
Parul
Period doubling bifurcations with small normal form coefficients
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/