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From: Ebsan Uddin on 8 May 2010 02:43
Sorry for the 2 year bump. But I have a similar hw problem. I just want to make sure I'm doing the right thing:

I've plotted the vector field and drew a phase portrait for Nonlinear Differential Equation. I need to plot the seperatrix by "picking an initial point close to the saddle point, and solving the IVP for t going from 0 to -20." According to my phase portrait I have two limits (0,0) and (3/2, 5/3). The seperatrix is a vector that passes (1/2, 0). I came up with this by looking at the phase portrait.

So if I'm correct all I have to do is pick an initial point around (1/2,0) such as (.501, .001) and solve with ode45.

Here's my code:
>>g = inline ('[ y(1)*(-1 + 2.5*y(1) - y(1)^2 - .3*y(2)); y(2)*(-1.5 + y(1))]', 't', 'y')
>>vectfield(g,0:.1:3,0:.1:2)
>>hold on
>> [ts,ys] = ode45(g,[0,-20],[.55;.01]);
plot(ys(:,1),ys(:,2))
>> axis ([0 3 0 2])
>> hold off

Thanks for the help in advance
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