Delay differential equations in general

The simplest such equation is

in which we understand r to be the per-capita reproduction of adults who require a developmental period of length r, and m is natural mortality. The still classic text in this area is Bellman and Cooke (1963). Nisbet and Gurney and their colleagues (see, for example, Gurney et al. (1983), Nisbet and Gurney (1983), Blythe et al. (1984), Nisbet et al. (1985)) have developed relatively complete methods for formulating population models with delays (see also May et al. (1974)). MacDonald (1989) shows how a single differential-difference equation can sometimes be converted to a system of linear equations without delays.

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