[BurningFrog]

Or one thing rotating.

You can imagine other cyclical processes, but I don't know any are realistic.

[pas]

Variable stars, something involving a cyclic phase transition (from silent to active and back). Something like the Type Ia supernova, where the dense white dwarf siphons off mass from its companion until it reaches the Chandrasekhar limit and bang.

[DFHippie]

The thing to explain then, in either the precession or the orbiting case, is the variability in the period.