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Create a vector field

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I am trying to create a vector field of a equation system, but I think that I have the slope wrong:
this is the system:
dx/dt = P-ay
dy/d t= Q-bx
And this my code:
x1=0;
x2=5;
y1=0;
y2=5;
N = 20;
x = linspace(x1,x2,N);
y = linspace(y1,y2,N);
[X,Y]= meshgrid(x,y);
U = -P+a.*y;
V = -Q+b.*x;
[U,V]=meshgrid(U,V);
quiver (app.Axes2,X,Y,U,V);
This is the field I have get it, which from my point of view it doesn't have too many sense:

Accepted Answer

David Goodmanson
David Goodmanson on 2 Mar 2021
Edited: David Goodmanson on 2 Mar 2021
Hi ALvaro,
The code below sets P=Q=0 to make the spacial dependence more clear.
Rather than meshgridding the 1d velocity vectors U1 and V1 to make U2 and V2 (I renamed them), you should define them directly as functions of the meshgridded matrix coordinates X and Y. Figure 2 satisfies the original equations and is much different than the original result of Figure(1).
There is also a question of overall sign reversal in the approach you used, but sign reversing back does not solve the problem. The real issue is not the sign but the method for calculating U and V.
a = .1;
b = .2;
P = 0;
Q = 0;
x1=-5;
x2=5;
y1=-5;
y2=5;
N = 20;
x = linspace(x1,x2,N);
y = linspace(y1,y2,N);
[X,Y]= meshgrid(x,y);
U1 = -P +a.*y; % sign reversed?
V1 = -Q +b.*x; % sign reversed?
[U2,V2]=meshgrid(U1,V1);
figure(1)
quiver (X,Y,U2,V2);
U3 = P -a.*Y;
V3 = Q -b.*X;
figure(2)
quiver (X,Y,U3,V3);
  3 Comments
Alvaro Mª Zumalacarregui Delgado
thanks a lot for you help!!

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