How to add arrows to solution trajectories using ode?

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Rose on 2 Sep 2014
Commented: Star Strider on 2 Sep 2014
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))
hold off
axis([0 15000 0 15000])

Accepted Answer

Star Strider
Star Strider on 2 Sep 2014
Edited: Star Strider on 2 Sep 2014
Meet the quiver function.
The odephas2 output function is also worth a look, although I’ve never used it.
Star Strider
Star Strider on 2 Sep 2014
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.

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