The generalized Turner-Bradley-Kirk-Pruitt equation

Abstract

Several recent results pertaining to nonlinear equations of ecology are applied to a generalization of the Turner-Bradley-Kirk-Pruitt (TBKP) equation, which illustrates a variety of interesting possibilities as regards persistence and extinction. The chief novelty consists in exploiting the value set of the equation, that is, the set of values taken on by the solution as t increases from 0 to ∞. This aspect of the subject depends on a new formulation of a condition that was first introduced by Vance and Coddington in 1989.