5.3 Example 3. Stable and Unstable limit cycles

These are animations of the system \(\dot{r}=r(r^2-3r+1),\dot{\theta }=1\) which exhibits a stable limit cycle of radius 1.



Stable limit cycle. \(\dot{r}=r(1-r^2), \dot{\theta }=1\)


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Unstable limit cycle. \(\dot{r}=-r(1-r^2), \dot{\theta }=1\)


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