# Can i plot different parameter differential equation phase plane in a line?

In order to compare with different parameter,can i use StreamPlot plot them in a line, for example:

$$\dot{x} = Ax$$

When $$A = [-1,0;0,-2]$$, i can use code as follows,

linearsys =
StreamPlot[{-x, -2 y}, {x, -14, 14}, {y, -14, 14},
StreamColorFunction -> "Rainbow", StreamPoints -> 24,
StreamScale -> 0.15, PerformanceGoal -> "Quality"];
Manipulate[
Show[linearsys,
ParametricPlot[
Evaluate[
First[{x[t], y[t]} /.
NDSolve[{x'[t] == -x[t], y'[t] == -2 y[t],
Thread[{x[0], y[0]} == point]}, {x, y}, {t, 0, T}]]], {t, 0,
T}, PlotStyle -> Red]], {{T, 0.1}, 0.1, 10}, {{point, {4, 4}},
Locator}, SaveDefinitions -> True]


If $$A = [\lambda_1,0;0,\lambda_2],~(\lambda_1,\lambda_2)=(1,2), ~(\lambda_1,\lambda_2)=(1,1),)$$, how can i use Table to plot StreamPlot and Manipulate respectively?

Let's rewrite your code to directly incorporate the matrix $$a$$:

a = {{-1, 0}, {0, -2}};
linearsys =
StreamPlot[a.{x, y}, {x, -14, 14}, {y, -14, 14},
StreamColorFunction -> "Rainbow", StreamPoints -> 24,
StreamScale -> 0.15, PerformanceGoal -> "Quality"];
Manipulate[
Show[linearsys, ParametricPlot[Evaluate[First[{x[t], y[t]} /.
NDSolve[{{x'[t], y'[t]} == a.{x[t], y[t]},
Thread[{x[0], y[0]} == point]}, {x, y}, {t, 0, T}]]], {t, 0, T},
PlotStyle -> Red]], {{T, 0.1}, 0.1, 10}, {{point, {4, 4}}, Locator}]


Now you can change the $$a$$ matrix at the top and it will plot the flow lines for that $$a$$ matrix.

BTW -- Ben, where did you get that code from? It is always good form to reference the source of code when it is not original.

• yeah,i forget the original,because i have make some change according mma official document.Thank you, i will try to find it. – Ben Nov 9 '18 at 14:08