Introduction and preview

Abstract

Imagine a biological population composed of adult and juvenile individuals. Let N(t) denote the density of adults at time t. Assume that the length of the juvenile period is exactly h units of time for each individual. Assume that adults produce offspring at a per capita rate α and that their probability per unit of time of dying is μ. Assume that a newborn survives the juvenile period with probability ρ and put r = αρ. Then the dynamics of N can be described by the differential equation

$$\dot N\left( t \right) = - \mu N\left( t \right) + rN\left( {t - h} \right)$$

((1.1))

which involves a nonlocal term, where N has argument t — h, since newborns become adults with some delay. So the rate of change of N involves the current as well as the past values of N. Such equations are called Retarded Functional Differential Equations (RFDE) or, alternatively, Delay Equations.