plotting phase portrait for a system

Question

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

Answer 1

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.