5.2 Example 2. Stable and Unstable limit cycles

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

And animation of the system \(\dot {r}=-r(1-r^2), \dot {\theta }=1\) where the limit cycle now becomes unstable.

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