From 927f4ef31d784dd2ce48f2e9e9ba369b04a31814 Mon Sep 17 00:00:00 2001 From: Dane Sabo Date: Mon, 30 Sep 2024 14:01:17 -0400 Subject: [PATCH] vault backup: 2024-09-30 14:01:16 --- .../2024-09-30 Limit Cycles.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) 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 a33fbc677..5ca21af73 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 @@ -12,7 +12,7 @@ Different forms: You can't identify if there is a limit cycle by using linearizing methods. # How do we find limit cycles? ## How do we rule out a closed loop? -### Dulac's Criterion: +### Bendixon's Criterion: If we have some flow field: $$ \dot{\vec{x}}= f(\vec x)$$ - If we can find a function $\zeta(x,y)$ such that $\nabla \cdot (\zeta f))$ does not change sign in some region of $R$, then there's no limit cycle in that region.