Periodic solution

Summary

A periodic solution of a differential equation is a solution defined for all times that repeats itself after a fixed time $T > 0$. For an autonomous system, a periodic solution that is not constant traces a periodic orbit in phase space. For an equation whose right-hand side is $T$-periodic in time, such as a periodically forced oscillator, one looks for solutions with the same period $T$. Periodic solutions model rhythms such as oscillating circuits, heartbeats and planetary motion.