I want to get a scaled vector field $\vec F=(x^2-x)i+(y^2-y)j$. The Fig should be like the attached Fig:

I want to get a scaled vector field $\vec F=(x^2-x)i+(y^2-y)j$. The Fig should be like the attached Fig:

[x,y] = meshgrid(-2:.16:2,-2:.16:2);

Fx = (x.*x-x);

Fy=y.*y-y;

figure;

quiver(x,y,Fx,Fy,'k','linewidth',1.2)

hold on

x=-2:0.01:2;

y=1-x;

plot(x,y,'k','linewidth',2);

Note that we have $div \vec F>0$ for $x+y>1$, $div \vec F<0$ for $x+y<1$ and $div \vec F=0$ on the line $x+y=1$ .

[John D'Errico]

A serious problem in your code is that you don't understand that x*x does NOT simply square the elements in the matrix. Instead it multiplies the matrix times itself, so a linear algebra operation. You need to use x.*x for that.

[Atom]

@John D'Errico Sorry, I have edited. Still I am not getting the desire plot.

[Dyuman Joshi]

What is the vector field scaled to?

The arrows of the vector field in the reference image appear to be of the same length.

Answer 1

[Sulaymon Eshkabilov]

Is this what you are trying to obtain:

[x, y] = meshgrid(-2:0.25:2);    % x and y values
F_x = 1*(x.^2 - x);              % The vector field of x
F_y = 1*(y.^2 - y);              % The vector field of y
F = F_x+F_y;
% Normalize the vectors
magnitude = sqrt(F_x.^2 + F_y.^2);
F_x_Nor = F_x ./ magnitude;
F_y_Nor = F_y ./ magnitude;

% Plot the scaled vector field
quiver(x, y, F_x_Nor, F_y_Nor);
hold on
X=-2:0.1:2;
Y=1-X;
plot(X,Y,'k','linewidth',2);
xlabel('x');
ylabel('y');
title('Scaled Vector Field: F = (x^2 - x) + (y^2 - y)');
axis([-2 2 -2 2])