I have the following ODE system
dx1 = -0.7 x1 y2 dy1 = 0.7 x1 y2 + 1.7 (1-x1-y1) y2 - y1 dx2 = -0.7 x2 y1 dy2 = 0.7 x2 y1 + 1.7 (1-x2-y2) y1 - y2
I have found that, for initial conditions of the type $x_1=1-y_1, x_2=1-y_2$, solutions either:
- reach a steady-state where $y_1=y_2=0$
- or reach a steady-state where $y_1,y_2>0$.
Now, I want to plot the plane of initial conditions $(y_1(0),y_2(0))$ and color each point in the plane blue or red depending on whether the steady-state falls in the first or second bucket.
I know how to use
streamplot to explore the phase-space of solutions but I am not sure how to go about plotting the regions depending on the steady-state value. Any ideas would be much appreciated.