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Pickett

2:10 AM

Ended up integrating many times around the limit cycle, sowing the time and then using the differences.

2 hours later…

Michael E2

3:45 AM

@Pickett How about something like this?

psol = ParametricNDSolveValue[
   {x'[t] == y[t], y'[t] == -1.5 (x[t]^2 - 1) y[t] - x[t], x[0] == x0,
     y[0] == y0,
    WhenEvent[y[t] < 0 && t > 0.001, "StopIntegration"]}, {x, y},
   {t, 0, 20}, {x0, y0}];

NestWhile[
 psol @@ Last /@ Through[#["ValuesOnGrid"]] &,
 psol[0.5, 0.],
 With[{p1 = foo = Last /@ Through[#1["ValuesOnGrid"]],
    p2 = Last /@ Through[#2["ValuesOnGrid"]]},
   EuclideanDistance[p1, p2]/Norm[p2] > 2 $MachineEpsilon] &,
 2, 1000]

The exit criterion 2 $MachineEpsilon might need to be increased in cases where the solution is not computed accurately.

2 hours later…

xzczd

5:35 AM

Hi, can someone help testing this piece of code, in either version?:

Clear@a
a /: (b : Except[a])[c__, a[d_]] := a[b[c, d]]
{x, a[1]}

In my v9.0.1, win 64bit, it outputs a[a[{x, 1}]]

but I just tested it in Wolfram Cloud, it outputs a[{x, 1}] as expected.

"in either version" <- Oh, I mean "in any version"

3 hours later…

Kuba

8:18 AM

@xzczd 10.3 gives a[a[{x, 1}]]

@xzczd There should be a duplicate topic, or closely related, there will be more heads in {x, a[1]} than you (I) think

a /: (b : Except[a | CompoundExpression])[c__, a[d_]] := (Print[b];
a[b[c, d]])

and it still prints additional IF :)

xzczd

8:38 AM

@Kuba Yeah, I have a feeling that I used to read a post related to this issue, but failed to find it. Let's wait for a moment to see if anyone can find it out.