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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:

Imgur

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?

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put on hold as off-topic by MarcoB, m_goldberg, Louis, Öskå, Edmund yesterday

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question cannot be answered without additional information. Questions on problems in code must describe the specific problem and include valid code to reproduce it. Any data used for programming examples should be embedded in the question or code to generate the (fake) data must be included." – MarcoB, m_goldberg, Louis, Öskå, Edmund
If this question can be reworded to fit the rules in the help center, please edit the question.

2  
related – Kuba Apr 23 '14 at 13:11
    
Take a look at StreamPlot. – Silvia Apr 23 '14 at 13:42