recurrent

Recurrent is an English adjective describing something that occurs again or repeatedly, or that returns after an interval. The term is used across disciplines to indicate repetition, regrowth, or relapse, and it can refer to events, conditions, processes, or patterns that recur with some regularity or after a pause.

In mathematics and computer science, a recurrence or recurrent element describes a relationship that defines a quantity in terms of previous values. A recurrence relation specifies each term as a function of earlier terms, yielding sequences such as the Fibonacci numbers. In stochastic processes, a state is described as recurrent if the process is certain to return to that state an infinite number of times. In machine learning, recurrent neural networks are architectures designed to handle sequential data by maintaining a hidden state. Variants such as long short-term memory (LSTM) and gated recurrent units (GRU) help manage long-range dependencies.

In medicine and epidemiology, recurrence refers to the return of a disease after a period of improvement or remission, also called relapse. Recurrence rates quantify how often a disease reappears after treatment, and causes can include residual pathogenic cells, resistance, or re-exposure. Recurrence affects management, prognosis, and surveillance, and terminology distinguishes recurrence from persistence or progression.

In astronomy, recurrent novae are systems in which a white dwarf accretes material from a companion and undergoes nova eruptions multiple times, separated by decades to a century.