# Phase Portrait Trajectories

How do I make a phase portrait which looks like the ones demonnstrated here? Not the fancy version where I can use the controls to change it, just a screen-shotted version of say a spiral point? Any help would be massively appreciated!

http://demonstrations.wolfram.com/PhasePortraitAndFieldDirectionsOfTwoDimensionalLinearSystems/

• Why don't you download the demonstration and study the code it contains? – m_goldberg Mar 12 '15 at 11:43
• Use StreamPlot function. – Vladimir Mar 12 '15 at 11:46
• Basins of Attraction – Artes Mar 12 '15 at 12:27
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Taking the code practically straight out of the author's demo:-

m = {{1, -3.5}, {2, -2}};

pt1 = {-5.1, 4.8};
pt2 = {4.9, 5.1};
pt3 = {-4.9, -5};
pt4 = {4.9, -5.2};

Show[VectorPlot[m.{x, y}, {x, -10, 10}, {y, -10, 10},
StreamPoints -> {{pt1, pt2, pt3, pt4}},
StreamStyle -> {Red, Thick}, ImageSize -> {460, 310}],
Graphics[
{Thick, Orange, Map[Line[{-100 #, 100 #}] &,
Select[Eigenvectors[m], (Im[#[[1]]] == 0 && Im[#[[2]]] == 0) &]]}],
PlotLabel -> Row[{Column[{Row[{Column[
{Style["\!$$\*OverscriptBox[\(x$$, $$.$$]\)", Italic],
Style["\!$$\*OverscriptBox[\(y$$, $$.$$]\)", Italic]}],
Column[{" = ", " = "}],
TableForm[m.{Style["x", Italic], Style["y", Italic]}] // N}]}], "  ",
Column[{"Eigenvalues:",
NumberForm[Chop@N@Eigenvalues[m], {4, 2}]}], "  ", ,
Column[{"Eigenvectors:",
NumberForm[Chop@N@Eigenvectors[m][[1]], {4, 2}],
NumberForm[Chop@N@Eigenvectors[m][[2]], {4, 2}] }]}]]