Plot a system of differential equations in a loop

Questions
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1

Hello,
I am having a problem to plot a system of two differential equations while one initial value is assigned values from a Table.
This is my code

g = 5/3;

c4 = 6;

smax = 10;

Rinit = 1.05;

Linit = 0.5;

t = Flatten@Table[Linit + i, {i, 0, 0.3, 0.1}];

Sol1 = NDSolveValue[{D1[s] == 
      2 (-1 + R[s]) R[
        s] (-(-1 + g) L[s] + 
         c4 ((-1 + R[s]) R[s]^3)^((1 - g)/2) (-2 + g) g L[s]^(2 - g) +
          c4 ((-1 + R[s]) R[s]^3)^((1 - g)/2) (-1 + g) g L[s]^-g), 
     N1[s] == -(1 + L[s]^2) (1 - g + 
         c4 (-1 + R[s])^(1/2 - g/2)
           R[s]^(-(3/2) (-1 + g)) (2 + 4 R[s] (-1 + g) - 3 g) g L[s]^(
          1 - g)), R'[s] == D1[s]/(\[Sqrt](D1[s]^2 + N1[s]^2)), 
     Derivative[1][L][s] == N1[s]/(\[Sqrt](D1[s]^2 + N1[s]^2)), 
     R[0] == Rinit, L[0] == #, 
     WhenEvent[
      D1[s] == 0, {smax = s, Print[N1[s]/D1[s]], "StopIntegration"}, 
      "DetectionMethod" -> "DerivativeSign"]}, {R, L}, {s, 0, 
     smax}] & /@ t

(*s1=ParametricPlot[Evaluate@Through[Sol1[{R[s],L[s]}]],{s,0,smax},\
PlotStyle\[Rule]Red,AxesLabel\[Rule]{R,L},AspectRatio\[Rule]Full,\
PlotRange\[Rule]All]*)

(*ParametricPlot[{Rsol[s],Lsol[s]},{s,0,smax},PlotStyle\[Rule]Red,\
AxesLabel\[Rule]{R,L},AspectRatio\[Rule]Full,PlotRange\[Rule]All]*)

I think there is a mistake on the ParametricPlot, but I am not sure.
I have included the file.
Thank you.

Code1 alt.nb (284 KB)

2

Agapi,

The code in the attached notebook does not match the code in the question. The usage of Through is incorrect. Check the documentation.

3

Thank you.
I have corrected the post so as to use the same symbols as the code.

4

Try

Plot[{
Sol1[[1,1]][s],Sol1[[1,2]][s],
Sol1[[2,1]][s],Sol1[[2,2]][s],
Sol1[[3,1]][s],Sol1[[3,2]][s],
Sol1[[4,1]][s],Sol1[[4,2]][s]},{s,0,smax}]

Then, if you really need to, you can modify that a tiny bit at a time and verify it works after each tiny change.

5

Thank you very much.
Is there a way to make the procedure a bit automated? I would like to be able to change the step and not having to type all these plots

6

A bit automated in what way?

If you can provide more detail about what you want then someone might be able to help.

7

Fair enough, but this is the starting point of something else I am trying to do. I might need to scan through hundreds of points and compare the results, first by plotting. That is why I am trying to do it a bit more automated or efficient if you like.
Thank you again for finding the time to answer my question.

8

If you can be more specific and precise about what you mean by “a bit more automated or efficient” then someone might be able to offer some idea.