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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)