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These are replies submitted by verdin

@one man 

I guess so however I don't know much about the Draghilev Method. I am not sure my system has continuous solutions. However in my system (x4,x5,x6,x7, a) I have 4 equations and 5 unknowns, so I expect it should work. The only problem could arise with the constraints 0.1<x4,x5,x6,x7<0.9, and a=0..5.


@one man 

yeah I realized it now, I overlooked it earlier. It seems that the system is most likely inconsistent. But there could be other set of (proper) solution too for which 0/0 does not occur.

Sorry to bother you again, but how can I obtain a parameteric variation between variable x8 and parameter a? Any remedy?

@one man 

Thank you very much. It worked very well. I am surprised the way fsolve did the job while the DirectSearch could not.

@one man 

Thank you for the clarification. I have implemented all of your suggestions and finally got a system in four variables x4, x5, x6, x7 and one parameter a.  Here is the file where I tried to solve it with the DirectSearch Method, however residues are still significant.

@one man 

Thanks for your reply.

I have  a problem with your suggestion. I forgot to mention that in my system f1, f2, ....f8 are nothing by dx1/dt, dx2/dt...dx8/dt, respectively. I am trying to obtain the steady-state solutions. For that I cannot implement your suggestion (to obtain x1 from f4 in tems of x4). Also I could not get much of Draghilev method. Is there any upper limit on number of variables and parameters and how to put my system in standard form to solve it by Draghilev method. Is there any .mla file (like Direct Search Method) which can be directly called to apply the Draghilev method.


@one man


First of all many thanks to you two to make me aware of such great methods.

I have tried with DirectSearch package, and unfortunately it is not giving me satisfactory results (the constraint is all x1, x2 .. x7 should be between 0.1 and 0.9, and x8 between 0.1 and 0.5. The solutions on back-substitution are not satisying the equations, leaving a significant remainder).

Now, I want to try Draghilev Method, I have looked into the examples provided on this forum, but could not get success. I have two objectives: First, I want to solve this system (restricting all x1, x2......x7 between 0.1 and 0.9, and x8 between 0.1 and 0.5), and second I want to plot variable x8 against 'a'. How can I do this efficiently. The worksheet is here

Many thanks in advance.


@Rouben Rostamian  Thank you for your comments.

I have fed my parameters into your file, but I am also unable to find the steady state solution.

However, I followed another approach (please take a look at dealing one equation at a time and I found the steady state. (I have taken only meaningful outcomes, and left the trivial steady state). My problem is that even after getting steady state I am unable to linearize my system. Is there any way or system cannot be linearized by any means?

@Rouben Rostamian  can you just show me how can I do it for a range of two parameters while keeping other fixed (take any choice of numeric values) or if it is not possible then how can I proceed for a set of parameters (take any choice of numeric values) as I am having difficultly (getting maple error ).

many thanks in advance.

@Rouben Rostamian  

@vv 4231

Hi all,

Earlier, I was doing some unncessary simplifcations due to which some problematic factors (which were rendering equations  undefined, might be cancelled out if taken care of properly ) were appearing in fractions and further it was leaving the problem at the dead-end. Here  i have provided the new dynamnical system which I want to linearize around steady-state(s). Please help me out.

Many thanks in advance.

@Rouben Rostamian  Thanks for pointing it out.

Now i have corrected the equations and it is Now I want to break my system into linear and nonlinear part. Help me in expressing logarithms and others variables appearing in denominator into series form. My objective is to investigate the eigenvalues of matrix obtained from linear part (whose elements are coefficient of x1(t), x2(t), and x3(t))  for different parameters values.

Many thanks.

@Carl Love 

Thanks a lot. You gave another insight on this problem. MATLAB gives  3.133160502850124, which is closer to what Axel is getting.Another thing which I noted time taken by Maple (17.098000 s) is greater than Matlab (0.065948 s) on an i5-CPU @ 3.10GHz × 4 , 8 GiB RAM.

@Axel Vogt 

Thanks. I follow your instructions till end, I got the decent graph but could you tell me how you got the final number.

one more thing i want to ask why did you not incorporate integral value at y = ymin which is -0.9994383218.

well matlab is giving the same value as you obtained.

@Preben Alsholm 

but my integral can easily be solved with matlab like a charm with the help of "integral2". why maple is not able to solve this numerically?


Methinks that after integrating inner integral with respect to y wud give an expression in x, on further integration with resepct to x with definite limits will come out with a number, so your assumption for the y's limit not being constant is ruled out. You  may check the link (fourth last eg where x limit is not constant) for the case where limit is not constant here

@Carl Love can you throw some light on my problem, I really need your view.


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