Timeline for On local attractivity of a coupled non-linear differential equation
Current License: CC BY-SA 3.0
9 events
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| Apr 11, 2018 at 21:47 | comment | added | Ludwig | Thanks a lot! See also this follow-up question which tries to address this point from a different angle. | |
| Apr 9, 2018 at 11:19 | history | edited | user539887 | CC BY-SA 3.0 |
Fixed colliding notation
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| Apr 8, 2018 at 10:45 | comment | added | user539887 | No, I don't have any idea. Incidentally, see my answer to your other question Behavior of a non-linear differential equation. | |
| Apr 3, 2018 at 5:13 | comment | added | Ludwig | Many thanks for the clarification! A last curiosity: In all my simulations I've noticed that (local) stability is also promoted by choosing $v$ and $w$ very different (i.e. choosing $|v-w|$ very large); hence I was wondering whether some sufficient conditions for local stability that involve the terms $v$ and $w$ could be derived. By chance, do you have any idea? | |
| Apr 3, 2018 at 5:07 | vote | accept | Ludwig | ||
| Mar 28, 2018 at 9:16 | comment | added | user539887 | I mean a theorem stating that if $\varphi$ [resp. $\psi$] is a solution of $x'= f(t, x)$ [resp. $x' = g(t,x)$] with $x(t_0) = x_0$ and $f(t,x) < g(t,x)$ for all $t$ then $\varphi(t) < \psi(t)$ for $t > t_0$ as long as both solutions are defined. Its proof is straightforward, but when we relax $<$ to $\le$ the situation changes: either one has to assume something additional (e.g. Lipschitz) or there are counterexamples (see math.stackexchange.com/questions/912468/… and math.stackexchange.com/questions/158332/…). | |
| Mar 27, 2018 at 14:32 | comment | added | Ludwig | Could you please elaborate a little more about the comparison property to solutions to ODE that you mentioned? Do you have a reference for this? Thanks! | |
| Mar 26, 2018 at 13:17 | comment | added | Ludwig | Thanks for your answer! Your argument is ingenious and looks technically sound to me (I need to carefully check the computations though)! I've also the impression that it could be "generalized" to provide conditions for stability in more complex cases (i.e. for systems with dimension larger than 3) | |
| Mar 25, 2018 at 10:43 | history | answered | user539887 | CC BY-SA 3.0 |