From a7a56fc8e5c3b03874ad4ead628cb110c6ae02e2 Mon Sep 17 00:00:00 2001 From: Dane Sabo Date: Mon, 23 Sep 2024 14:12:51 -0400 Subject: [PATCH] vault backup: 2024-09-23 14:12:51 --- .../2024-09-23 Temporary Title.md | 11 ++++++++++- 1 file changed, 10 insertions(+), 1 deletion(-) diff --git a/300s School/ME 2016 - Nonlinear Dynamical Systems 1/2024-09-23 Temporary Title.md b/300s School/ME 2016 - Nonlinear Dynamical Systems 1/2024-09-23 Temporary Title.md index c153c5832..a94ed9fbb 100644 --- a/300s School/ME 2016 - Nonlinear Dynamical Systems 1/2024-09-23 Temporary Title.md +++ b/300s School/ME 2016 - Nonlinear Dynamical Systems 1/2024-09-23 Temporary Title.md @@ -88,4 +88,13 @@ For $\bf J$: - $\Delta = \pm\omega^2$ Then: - $\theta$ is 0, $\Delta = \omega^2 >0$, spiral. Stable -- $\theta = n \pi$, $\Delta = - \omega^2 <0$, saddle. Unstable \ No newline at end of file +- $\theta = n \pi$, $\Delta = - \omega^2 <0$, saddle. Unstable +--- +# Competing Species Problems +We have a Species X vs. Species Y. +$$\dot x = x(\beta-\delta x -\gamma y) = \beta x - \delta x^2 - \gamma xy$$ +$$\dot y = y(b - d y - c x) = by - dy^2 -cxy$$ +>[!note] Coupling Terms +>$\gamma x y$ and $c x y$ are coupling terms. +>These equations are coupled because of these. Without them x and y would just be doing their own thing. +