vault backup: 2024-09-23 14:38:31

2024-09-23 14:38:31 -04:00 · 2024-09-23 14:38:31 -04:00 · f4fc6160dc
commit f4fc6160dc
parent a7a56fc8e5
1 changed files with 6 additions and 1 deletions
--- a/1/2024-09-23
+++ b/1/2024-09-23
@ -97,4 +97,9 @@ $$\dot y = y(b - d y - c x) = by - dy^2 -cxy$$
 >[!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.
-
+## Computing our Jacobian
+$$ {\bf J} = 
+\left[ \matrix{ \frac{\partial P}{\partial x} &  \frac{\partial P}{\partial y} \\ \frac{\partial Q}{\partial x} & \frac{\partial Q}{\partial y}} \right] = 
+\left[ \matrix{ \beta -2\delta x - \gamma y & -\gamma x\\ - c y & b - 2dy - cx} \right]  
+ $$
+ Now we can actually do stuff with this in SymPy