recurrend

Recurrend is a term used in discussions of dynamic systems to denote a factor, mechanism, or signal that generates or sustains recurrence in a process. A recurrend is more than a mere repeating event; it is the source or trigger that causes states to reappear, either on a regular schedule or in a more irregular but persistent pattern.

In mathematical modeling, recurrends can be internal, such as memory terms in a recurrence relation or internal feedback loops, or external, such as seasonal or periodic forcing. They are distinguished from the recurring events themselves by playing an active role in producing recurrence. The study of recurrends helps separate the causes of reappearance from the phenomenology of the recurrence.

The term is used in modern, interdisciplinary discussions of complex systems and has appeared in contexts such as time-series analysis, epidemiology, and network dynamics. It is related to but distinct from recurrence, recurrent processes, and feedback mechanisms. Related concepts include recurrence relations, attractors, and seasonal forcing.