Is the system on slide 5 stable?

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Q Is the system on slide 5 stable?

A First of all you should question about stability of the euquilibrium points of the system. Such points are (+- n*pi, 0).

As you can see from the phase portrait, for n=0 and n even, you have that the trajectories circle around the points: these are therefore centers, and are stable equilibrium points.

For n odd, the points are called saddles: from the phase portrait you can see that trajectories coming from a direction of -45deg converge to the point, while the all the others will diverge. Such points are not stable.