a,b are parameters. While entering this map into matcontm, I tried to give the saddle fixed point values and suppose we have a condition on the parameters as a = b + 3 (at which i obtain saddle fixed points) , so I was thinking of giving a single value of b and then it could automatically calculate the value of a. While calculating the invariant manifolds, it gives me an error in MATLAB saying "Error while evaluating UIControl Callback" but it works fine if I give the value of 'a' numerically?
and also while continuation of say homoclinic orbit, it would always follow the condition a = b+ 3 and I would be getting the required curve
Do I always have to enter numerical values of parameters in the system box? would entering algebraic expressions involving other parameters wll not work?
Thanks!
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a,b are parameters. While entering this map into matcontm, I tried to give the saddle fixed point values and suppose we have a condition on the parameters as a = b + 3 (at which i obtain saddle fixed points) , so I was thinking of giving a single value of b and then it could automatically calculate the value of a. While calculating the invariant manifolds, it gives me an error in MATLAB saying "Error while evaluating UIControl Callback" but it works fine if I give the value of 'a' numerically?
and also while continuation of say homoclinic orbit, it would always follow the condition a = b+ 3 and I would be getting the required curve
Do I always have to enter numerical values of parameters in the system box? would entering algebraic expressions involving other parameters wll not work?
Oh thanks!. Is there any variable which controls the tolerance of |a - (b+3)| or if it was a more complicated equation? I want to make the tolerance as less as 10^-11.
Thanks!
Last edit: Phenom 2020-02-18
If you would like to refer to this comment somewhere else in this project, copy and paste the following link:
From: Phenom sphenom@users.sourceforge.net
Sent: Tuesday, February 18, 2020 4:56 AM
To: [matcont:discussion]
Subject: [matcont:discussion] Setting up algebraic expression of a parameter in a map in Matcontm starter window.
Oh thanks!. Is there any variable which controls the tolerance of |a - (b+3)| or if it was a more complicated equation? I want to make the tolerance as less as 10^-11.
Suppose I am continuing homoclinic tangency in the Henon map. I got the tangency curve in two parameters. Now I took a point on the tangency curve and checked whether I am getting a tangnecy or not. I do get tangency! (a single tangential intersection between the stable and unstable manifolds would imply infinitely many tangencies) but as I move closer to the fixed point, I observe that there is still a small gap between the manifolds (the more we go near to fixed point, the gap increases) and I think that it is fine but I want to control the gap to some tolerance near the fixed point.
Is there any variable responsible for this (which can control the distance or gap between the stable and unstable manifold near to the tangency)? like say I want the tangency of the stable and unstable manifold of the saddle fixed point close as 10^-8. This also means that parameters will also change now!
Thanks Hil!
If you would like to refer to this comment somewhere else in this project, copy and paste the following link:
So here you need to look at the defining system that we use, which basically consists of a finite piece of a discrete orbit whose first and last point lie within the linear stable and unstable subspaces. So there is no direct parameter to control this.
The remedy is to use more points for the orbit piece, so you will be closer to the homoclinic tangency.
This will be slower though...
Best, Hil
From: Phenom sphenom@users.sourceforge.net
Sent: Friday, February 21, 2020 6:02 AM
To: [matcont:discussion]
Subject: [matcont:discussion] Setting up algebraic expression of a parameter in a map in Matcontm starter window.
Sorry for that!
Suppose I am continuing homoclinic tangency in the Henon map. I got the tangency curve in two parameters. Now I took a point on the tangency curve and checked whether I am getting a tangnecy or not. I do get tangency! (a single tangential intersection between the stable and unstable manifolds would imply infinitely many tangencies) but as I move closer to the fixed point, I observe that there is still a small gap between the manifolds (the more we go near to fixed point, the gap increases) and I think that it is fine but I want to control the gap to some tolerance near the fixed point.
Is there any variable responsible for this (which can control the distance or gap between the stable and unstable manifold near to the tangency)? like say I want the tangency of the stable and unstable manifold of the saddle fixed point close as 10^-8. This also means that parameters will also change now!
with parameters R = -0.3, S = -0.1, b = 0.5401 with saddle fixed point (-5.1336,-5.1336). Trying manually by coding, I can obtain the stable and unstable manifolds of the saddle point. But trying it in Matcontm: I am not able to compute the unstable manifold (it says no ocnvergence), the stable manifold is computed. Below are some snapshots. I am not sure why?
Are you sure that you actually have a fixed point?
Setting x=y, and solving for y, I find completely different roots for these parameter values.
That means that the first point is mapped to somewhere else.
There is a check on whether the input is a fixed point but this was incorrectly implemented.
init_FPm_1DMan.m, line 33; should read (norm was missing)
if norm(feval(man_ds.func,0,man_ds.x0, man_ds.P0{:})-man_ds.x0) > opt_man.eps
Best regards, Hil Meijer
From: Phenom sphenom@users.sourceforge.net
Sent: Thursday, February 27, 2020 5:27 AM
To: [matcont:discussion]
Subject: [matcont:discussion] Setting up algebraic expression of a parameter in a map in Matcontm starter window.
with parameters R = -0.3, S = -0.1, b = 0.5401 with saddle fixed point (-5.1336,-5.1336). Trying manually by coding, I can obtain the stable and unstable manifolds of the saddle point. But trying it in Matcontm: I am not able to compute the unstable manifold (it says no ocnvergence), the stable manifold is computed. Below are some snapshots. I am not sure why?
Sorry, I jumbled up the numbers while typing. The saddle fixed point is (-1.53333,-1.53333) for R = -0.3, S =-0.1, b = 0.5401. Even then I got the plot in actual coding but not in MATCONTM (it says no convergence/ norm but kind of plots the stable manifold)? do you have any thoughts why this is happening?
While I like to help, I can't do this. You're still posting a request where the coordinates are not a fixed point.
Set x-->y (because of the first equation) and insert it into the second equation. Then next compute the roots of this cubic polynomial.
Best, Hil
From: Phenom sphenom@users.sourceforge.net
Sent: Tuesday, March 3, 2020 5:32 AM
To: [matcont:discussion]
Subject: [matcont:discussion] Setting up algebraic expression of a parameter in a map in Matcontm starter window.
Suppose we consider the Henon map
x' = 1 - ax^2 + y
y' = b x
a,b are parameters. While entering this map into matcontm, I tried to give the saddle fixed point values and suppose we have a condition on the parameters as a = b + 3 (at which i obtain saddle fixed points) , so I was thinking of giving a single value of b and then it could automatically calculate the value of a. While calculating the invariant manifolds, it gives me an error in MATLAB saying "Error while evaluating UIControl Callback" but it works fine if I give the value of 'a' numerically?
and also while continuation of say homoclinic orbit, it would always follow the condition a = b+ 3 and I would be getting the required curve
Do I always have to enter numerical values of parameters in the system box? would entering algebraic expressions involving other parameters wll not work?
Thanks!
Sorry that won't work. You need to specify values.
Alternatively you create a new different system where you define b=a+3.
Best Hil
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From: Sishu sphenom@users.sourceforge.net
Sent: Monday, February 17, 2020 3:33:49 AM
To: [matcont:discussion] 762214@discussion.matcont.p.re.sourceforge.net
Subject: [matcont:discussion] Setting up algebraic expression of a parameter in a map in Matcontm starter window.
Suppose we consider the Henon map
x' = 1 - ax^2 + y
y' = b x
a,b are parameters. While entering this map into matcontm, I tried to give the saddle fixed point values and suppose we have a condition on the parameters as a = b + 3 (at which i obtain saddle fixed points) , so I was thinking of giving a single value of b and then it could automatically calculate the value of a. While calculating the invariant manifolds, it gives me an error in MATLAB saying "Error while evaluating UIControl Callback" but it works fine if I give the value of 'a' numerically?
and also while continuation of say homoclinic orbit, it would always follow the condition a = b+ 3 and I would be getting the required curve
Do I always have to enter numerical values of parameters in the system box? would entering algebraic expressions involving other parameters wll not work?
Thanks!
Setting up algebraic expression of a parameter in a map in Matcontm starter window.
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Oh thanks!. Is there any variable which controls the tolerance of |a - (b+3)| or if it was a more complicated equation? I want to make the tolerance as less as 10^-11.
Thanks!
Last edit: Phenom 2020-02-18
I do not understand the question.
From: Phenom sphenom@users.sourceforge.net
Sent: Tuesday, February 18, 2020 4:56 AM
To: [matcont:discussion]
Subject: [matcont:discussion] Setting up algebraic expression of a parameter in a map in Matcontm starter window.
Oh thanks!. Is there any variable which controls the tolerance of |a - (b+3)| or if it was a more complicated equation? I want to make the tolerance as less as 10^-11.
Thanks,
Sishu
Setting up algebraic expression of a parameter in a map in Matcontm starter window.
Sent from sourceforge.net because you indicated interest in https://sourceforge.net/p/matcont/discussion/762214/
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Sorry for that!
Suppose I am continuing homoclinic tangency in the Henon map. I got the tangency curve in two parameters. Now I took a point on the tangency curve and checked whether I am getting a tangnecy or not. I do get tangency! (a single tangential intersection between the stable and unstable manifolds would imply infinitely many tangencies) but as I move closer to the fixed point, I observe that there is still a small gap between the manifolds (the more we go near to fixed point, the gap increases) and I think that it is fine but I want to control the gap to some tolerance near the fixed point.
Is there any variable responsible for this (which can control the distance or gap between the stable and unstable manifold near to the tangency)? like say I want the tangency of the stable and unstable manifold of the saddle fixed point close as 10^-8. This also means that parameters will also change now!
Thanks Hil!
So here you need to look at the defining system that we use, which basically consists of a finite piece of a discrete orbit whose first and last point lie within the linear stable and unstable subspaces. So there is no direct parameter to control this.
The remedy is to use more points for the orbit piece, so you will be closer to the homoclinic tangency.
This will be slower though...
Best, Hil
From: Phenom sphenom@users.sourceforge.net
Sent: Friday, February 21, 2020 6:02 AM
To: [matcont:discussion]
Subject: [matcont:discussion] Setting up algebraic expression of a parameter in a map in Matcontm starter window.
Sorry for that!
Suppose I am continuing homoclinic tangency in the Henon map. I got the tangency curve in two parameters. Now I took a point on the tangency curve and checked whether I am getting a tangnecy or not. I do get tangency! (a single tangential intersection between the stable and unstable manifolds would imply infinitely many tangencies) but as I move closer to the fixed point, I observe that there is still a small gap between the manifolds (the more we go near to fixed point, the gap increases) and I think that it is fine but I want to control the gap to some tolerance near the fixed point.
Is there any variable responsible for this (which can control the distance or gap between the stable and unstable manifold near to the tangency)? like say I want the tangency of the stable and unstable manifold of the saddle fixed point close as 10^-8. This also means that parameters will also change now!
Thanks Hil!
Setting up algebraic expression of a parameter in a map in Matcontm starter window.
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/
Thanks Hil.
I was trying the following map
x' = y
y' = ((-S(b+1))^3 + R(b+1)^2)/(R^3) - bx - y^2 +Rxy + S(y^3)
with parameters R = -0.3, S = -0.1, b = 0.5401 with saddle fixed point (-5.1336,-5.1336). Trying manually by coding, I can obtain the stable and unstable manifolds of the saddle point. But trying it in Matcontm: I am not able to compute the unstable manifold (it says no ocnvergence), the stable manifold is computed. Below are some snapshots. I am not sure why?
Dear Phenom(Sishu),
Are you sure that you actually have a fixed point?
Setting x=y, and solving for y, I find completely different roots for these parameter values.
That means that the first point is mapped to somewhere else.
There is a check on whether the input is a fixed point but this was incorrectly implemented.
init_FPm_1DMan.m, line 33; should read (norm was missing)
if norm(feval(man_ds.func,0,man_ds.x0, man_ds.P0{:})-man_ds.x0) > opt_man.eps
Best regards, Hil Meijer
From: Phenom sphenom@users.sourceforge.net
Sent: Thursday, February 27, 2020 5:27 AM
To: [matcont:discussion]
Subject: [matcont:discussion] Setting up algebraic expression of a parameter in a map in Matcontm starter window.
Thanks Hil.
I was trying the following map
x' = y
y' = ((-S(b+1))^3 + R(b+1)^2)/(R^3) - bx - y^2 +Rxy + S(y^3)
with parameters R = -0.3, S = -0.1, b = 0.5401 with saddle fixed point (-5.1336,-5.1336). Trying manually by coding, I can obtain the stable and unstable manifolds of the saddle point. But trying it in Matcontm: I am not able to compute the unstable manifold (it says no ocnvergence), the stable manifold is computed. Below are some snapshots. I am not sure why?
Attachments:
[https://sourceforge.net/p/matcont/discussion/762214/thread/02e8468c3f/3141/attachment/starter%20wind%20param.PNG]
) (18.5 kB; image/png)
- starter_box_unst.PNG (5.6 kB; image/png)
- unst_mnfld_box.PNG (16.4 kB; image/png)
Setting up algebraic expression of a parameter in a map in Matcontm starter window.
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Hi Hil,
Sorry, I jumbled up the numbers while typing. The saddle fixed point is (-1.53333,-1.53333) for R = -0.3, S =-0.1, b = 0.5401. Even then I got the plot in actual coding but not in MATCONTM (it says no convergence/ norm but kind of plots the stable manifold)? do you have any thoughts why this is happening?
Please find the attached plots.
Thanks,
Phenom
Last edit: Phenom 2020-03-03
While I like to help, I can't do this. You're still posting a request where the coordinates are not a fixed point.
Set x-->y (because of the first equation) and insert it into the second equation. Then next compute the roots of this cubic polynomial.
Best, Hil
From: Phenom sphenom@users.sourceforge.net
Sent: Tuesday, March 3, 2020 5:32 AM
To: [matcont:discussion]
Subject: [matcont:discussion] Setting up algebraic expression of a parameter in a map in Matcontm starter window.
Hi Hil,
Thanks,
Sishu
Attachments:
Setting up algebraic expression of a parameter in a map in Matcontm starter window.
Sent from sourceforge.net because you indicated interest in https://sourceforge.net/p/matcont/discussion/762214/
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