From fd7430afead7827ae0cb7f401a6af6959a4fbefe Mon Sep 17 00:00:00 2001 From: Dane Sabo Date: Mon, 30 Sep 2024 13:20:38 -0400 Subject: [PATCH] vault backup: 2024-09-30 13:20:38 --- .../2024-09-30 Limit Cycles.md | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/300s School/ME 2016 - Nonlinear Dynamical Systems 1/2024-09-30 Limit Cycles.md b/300s School/ME 2016 - Nonlinear Dynamical Systems 1/2024-09-30 Limit Cycles.md index cacaa97b..5c85cc31 100644 --- a/300s School/ME 2016 - Nonlinear Dynamical Systems 1/2024-09-30 Limit Cycles.md +++ b/300s School/ME 2016 - Nonlinear Dynamical Systems 1/2024-09-30 Limit Cycles.md @@ -35,3 +35,7 @@ $\alpha e^{\alpha x} y + 2 y e^{\alpha x} - e^{\alpha x}$ $e^{\alpha x}((\alpha+2) y -1)$ Now let $\alpha = -2$ $\nabla \cdot (\zeta f) = e^{-2 x}$ + +Now a special note: These functions can define where limit cycles can't be. If the function doesn't change sign for a subset of R, there can't be a limit cycle contained in that subset. There CAN be a limit cycle that crosses the point the function changes sign. +### Lyapunov Function +Aleksander Lyapunov (Liapunov) \ No newline at end of file