I want to plot phase portrait for below system \begin{cases} d\phi/d\zeta=Z \\ dZ/d\zeta=a\phi+b\phi^2+c\phi^3 \end{cases} a=-0.13 b=-0.07 c=-2.83 Can any body help me? Thanks
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2You can't really, if $a, b$ and $c$ are unknown. – Rebellos Dec 07 '18 at 09:37
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Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please [edit] the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers. – José Carlos Santos Dec 07 '18 at 09:37
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With the MATHEMATICA script
tmax = 10;
gr1 = StreamPlot[{-0.13 phi - 0.07 phi^2 - 2.83 phi^3, z}, {z, -1, 1}, {phi, -1, 1}];
sol = NDSolve[
{phi'[t] == z[t],
z'[t] == -0.13 phi[t] - 0.07 phi[t]^2 - 2.83 phi[t]^3,
z[0] == 0.6, phi[0] == 0.6}, {z, phi}, {t, 0, tmax}][[1]];
gr2 = ParametricPlot[Evaluate[{z[t], phi[t]} /. sol], {t, 0, tmax}, PlotStyle -> Red];
Show[gr1, gr2]
we get the stream flow in blue and a typical orbit in red.
Cesareo
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