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. \(\dot {r}=r(1-r^2), \dot {\theta }=1\) Pause Play Restart Step forward Step back

Unstable limit cycle. \(\dot {r}=-r(1-r^2), \dot {\theta }=1\) Pause Play Restart Step forward Step back