The Beverton-Holt equation from a Control Theory point of view

This paper is devoted to develop some ldquoad-hocrdquo Control Theory formalism useful for the famous Beverton-Holt Equation arising in population dynamics. In particular, the inverse equation is redefined for a finite set of consecutive samples under the equivalent form of a discrete linear dynamic system whose input sequence is defined by the sequence of carrying capacity gains and the unforced dynamics is directly related to the intrinsic growth rate. For that purpose, the environment carrying capacity gains are allowed to be time-varying and designed for control purposes. The controllability and stability properties of the dynamic system associated with the Beverton-Holt inverse equation allow extrapolate in a simple dual way the above properties to the standard Beverton-Holt equation.