How to add arrows to solution trajectories using ode?

I have a system of two odes and i want to plot the phase portrait with arrows and clearly representing the stable and unstable steady states. The problem is that i am getting the solution trajectories but without arrows. So it is very difficult to see which steady state is stable. Here is the ode system:

    function dy = twodim(~,y, mu, d1, d2, K, n, p, sigma1, sigma2)

    dy(1,1) = mu.*((y(1) + y(2)).^n)./(K.^n + (y(1) + y(2)).^n) - d1.*y(1) - y(1).*(sigma1 - sigma2.*(y(2)./(y(1) + y(2) + 1e-12))) ;

     dy(2,1) = y(1).*(sigma1 - sigma2.*(y(2)./(y(1) + y(2) + 1e-12))) - (p + d2).*y(2);

Below is the part of the code I use to draw the solution trajectories:

    mu = 2000;
    K = 27000;
    d1 = 0;
    d2 = 0;
    sigma1 = 0.25;
    sigma2 = 0.75;
    p = 0.24;
    n = 1;

    close all; hold on
    for a = 0:5250:15000
    for b = 0:5250:15000
    [t, y] = ode45(@(t,y)twodim(t,y, mu, d1, d2, K, n, p, sigma1, sigma2), 0:0.2:15000, [a; b]);
    plot(y(:,1), y(:,2))
    end
    end
    hold off
    axis([0 15000 0 15000])

Answer 1

[Star Strider]

Meet the quiver function.

The odephas2 output function is also worth a look, although I’ve never used it.

[Rose]

i tried the quiver function but it doesn't draw arrows along with the solution trajectories only, it draws them on the whole grid.

[Star Strider]

I’m not quite sure I understand the problem, or your ODE, so I don’t know if this is what you want. It is sometimes necessary to experiment with quiver:

arowscal = 10;
quiver(y(:,1), y(:,2), gradient(-y(:,1)), gradient(y(:,1)), arowscal )

The ‘arowscal’ parameter lengthens the arrows so you can see them.

I’m not aware of any other way to add arrows to plots, although there may be some File Exchange routines that will do it.