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I want to solve and plot the solutions of the following system on the triangle simplex:

x'[t] == x[t]*(2*x[t] - 2)
y'[t] == y[t]*(2*x[t]) 
z'[t] == z[t]*(2*x[t])

It is assumed that x[t] + y[t] + z[t] == 1 for all times t.

I am looking for output similar to this:


I;m also interested in plotting the frequency changes of x[t],y[t] and z[t] over time. That is, given an initial value, I want to find how the frequencies vary over time?

share|improve this question
related – Kuba Apr 23 '14 at 13:11
Take a look at StreamPlot. – Silvia Apr 23 '14 at 13:42

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