# Why my stable point is not in [0,0]?

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Frantisek Stloukal on 29 Apr 2021
Hi, I am trying to plot this phase-time portrait by code I have found here. I don't know why my stable point is not in [0,0] but is shifted to aproximately [11,11]. Any ideas how to repair this problem ? Thanks a lot.
the code:
figure()
%phase-time
[X1,X2] = meshgrid(-5:0.5:5);
xs = arrayfun(@(x,y) {odeFun([],[x,y])}, X1, X2);
x1s = cellfun(@(x) x(1), xs);
x2s = cellfun(@(x) x(2), xs);
quiver(x1s, x2s)
xlabel('x_1')
ylabel('x_2')
axis tight
function dxdt = odeFun(t,x)
global A %pre-difined matrix of autonomous system of ODE's
dxdt(1) = A(1,1)*x(1)+A(1,2)*x(2);
dxdt(2) = A(2,1)*x(1)+A(2,2)*x(2);
end
jessupj on 29 Apr 2021
Edited: jessupj on 29 Apr 2021
my guess is that (0,0) corresponds to [X1(11,11),X2(11,11)]. that is, the plot is plotting arrows at locations based on the index of the vectors since you are not telling it what the coordinates are.
try reading the documetnation of quiver to add the location arguments, probably something like
quiver( x1s,x2s, X1, X2)
Frantisek Stloukal on 30 Apr 2021
Edited: Frantisek Stloukal on 30 Apr 2021
I have tried that. The portrait center is now in [0,0] as it should be, although it looks like a distorted banana :D What is interesting is that when equilibrium points are type center or focus it works (when eigen numbers are complex), but when saddle or node it by some reason colaps into this:

Jan on 30 Apr 2021
Your command for creating the diagram does not get any information about the X and Y coordiantes:
quiver(x1s, x2s)
Then it assume, that the coordinates are going from 1 to the number of elements in each direction.
Provide the X and Y coordinates, if you want so see them:
quiver(X1, X2, x1s, x2s)
Trying to run your code produces an errort message, e.g. due to the missing variable A. So please test this by your own.
jessupj on 30 Apr 2021
try@Jan's suggestion... mine reversed the position and arrow vectors. ALWAYS read doumentation on matlab functions.
Frantisek Stloukal on 2 May 2021
Works pretty good for me. Thank you @Jan.

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