Editing Recurrence relation (section)

=== Mathematical biology ===
Some of the best-known difference equations have their origins in the attempt to model [[population dynamics]]. For example, the [[Fibonacci number]]s were once used as a model for the growth of a rabbit population.

The [[logistic map]] is used either directly to model population growth, or as a starting point for more detailed models of population dynamics. In this context, coupled difference equations are often used to model the interaction of two or more [[population]]s. For example, the [[Nicholson–Bailey model]] for a host-[[parasite]] interaction is given by

:<math>N_{t+1} = \lambda N_t e^{-aP_t} </math>
:<math>P_{t+1} = N_t(1-e^{-aP_t}), </math>

with <math>N_t</math> representing the hosts, and <math>P_t</math> the parasites, at time <math>t</math>.

[[Integrodifference equation]]s are a form of recurrence relation important to spatial [[ecology]]. These and other difference equations are particularly suited to modeling [[voltinism|univoltine]] populations.