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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.