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An orbit that returns exactly after a nonzero period. In discrete time a periodic point satisfies for some positive integer ; a fixed point is the period-one case.
wp-math-periodic-orbitwp-math-orbit-dynamicsmit-ocw-nonlinear-dynamicsEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
A periodic orbit is an orbit that returns exactly after a nonzero period; not every recurrent orbit is periodic.
The target is a member or subtype of the broader source class.
wp-math-periodic-orbitwp-math-orbit-dynamicsmit-ocw-nonlinear-dynamicsEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Periodic orbits can be analyzed for orbital or transverse stability; periodicity alone does not imply attraction or stability.
The target represents a state, property, observable, or state-dependent description associated with the source system or theory.
wp-math-periodic-orbitwp-math-stability-theorymit-ocw-nonlinear-dynamics