Hi,
I’m novice in Wolfram Mathematica Language and I have to draw two differential equations.
They represent the Lokta Model.
Here the equations :
x˙=x(1−y)
y˙=y(−λ+x)
And I have to draw it like in this page : Le modèle proie-prédateur de Lotka-Volterra - Experimentarium Digitale
I really hope you can help me because it’s very difficult for a novice in Wolfram!
Thank you for your help.
Regards.
That is not quite a project for a novice. However, here is a way:
Manipulate[
StreamPlot[{x (1 - y), y (-\[Lambda] + x)},
{x, 0, 2}, {y, 0, 2}],
{{\[Lambda], 1}, 0, 2}]
Yeah I know but I have to do it.
Thank you i just try your code!
Now the most important for my document it’s the diagram with (x+y) in function of time.
The graph under on the website cnrs.
Have you an idea or something to help me on that?
Sorry I don’t want to take your time if you can’t it’s okay 
@Gianluca Gorni : Nice - simple, but very intuitive!
I guess for the full solution one needs ParametricNDSolve and friends:
ClearAll["Global`*"]
(* define the Lotka model: *)
x0 = 2; y0 = 1.5;
tRange = {t, 0, 30};
deq = {x'[t] == x[t] (1 - y[t]), y'[t] == y[t] (-\[Lambda] + x[t]), x[0] == x0, y[0] == y0};
(* solve it: *)
lotka = ParametricNDSolveValue[deq, {x[t], y[t]}, tRange, {\[Lambda]}];
(* show the solution: *)
Manipulate[ParametricPlot[lotka[\[Lambda]], Evaluate@tRange, PlotRange -> {{0, 11}, {0, 4.3}}, PerformanceGoal -> "Quality",
ImageSize -> Large, GridLines -> {{x0}, {y0}}, Epilog -> {Dashed, Red,
InfiniteLine[{{\[Lambda], 0}, {\[Lambda], 1}}]}], {\[Lambda], .3, 5}]
Manipulate[
Plot[Evaluate@lotka[\[Lambda]], tRange, Filling -> Bottom,
PlotRange -> {0, Automatic}, ImageSize -> Large], {\[Lambda], 0, 5}]
Thank you so much Henrik Schachner and Gianluca Gorni for your help.
I really have to learn this language because it seems so good to us it when you know his capacities.
Have a good day.
Thanks again!
