Timeline for WhenEvent&NDSolve: How to detect saddle point?
Current License: CC BY-SA 4.0
5 events
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| Jul 5, 2019 at 17:38 | comment | added | Michael E2 |
@UlrichNeumann OK, I'll try to think about sgn[t]~Sign[x'[t]] -- discontinuities can be tricky. I don't think in every case there is a solution to an ODE with discontinuous coefficients. Plot x'[t] over a small range including the saddle: it decreases to zero (approximately) and then increases immediately with an angle like absolute value. A discrete plot should show a line segment with a positive slope, since an instantaneously zero slope is impossible to draw via line segments (which is what Plot[] does).
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| Jul 5, 2019 at 17:31 | comment | added | Ulrich Neumann |
@ Michael E2 : sgn[t]~Sign[x'[t]] is what I'm looking for. I agree that x''[t] must change sign in the saddle point. In the plot of your answer I see a positive slope of the blue curve near the saddle.
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| Jul 5, 2019 at 17:24 | comment | added | Michael E2 |
@UlrichNeumann The saddle event presumes that sgn[t] changes sign. If you do not change its sign, then x''[t] will not change sign and there will be an extremum, not a saddle. I'm not sure why you want sgn[t] not to change at a potential saddle, but if it's to prevent saddles in the solution, then it seems to me it's working (except my variables extrema and saddle no longer count extremas and saddles, which seems unimportant and/or fixable).
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| Jul 5, 2019 at 17:04 | comment | added | Ulrich Neumann |
@ MichaelE2 Thank you for your answer, I have to analyse in detail! The saddle is well detected but sgn shouldn't change!. I changed the saddle -event to s[t]-> s[t] but doesn't work .
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| Jul 5, 2019 at 16:51 | history | answered | Michael E2 | CC BY-SA 4.0 |