Global Stability in a Nonlinear Difference-Delay Equation Model of Flour Beetle Population Growth

Here L t , P t , and At are the number of feeding larvae. pupae, and non-feeding larvae, and adults. respectively, at time t; the unit of time is taken to be the feeding larval maturation period so that after one unit of time, a larva either dies or survives and pupates. This unit of time is also the time spent as a non-feeding larva, pupa and callow (young adult). b is a positive constant describing the number of eggs laid per adult per unit of time. System (1.1)-(1.3) models a class of flour beetles of the genus Tribolium that are cannibalistic (Park et al. 1965). For these flour beetles, adults may feed on eggs, larvae. pupae and callows, while larvae may eat eggs, pupae, and callows. Neither larvae nor adults eat mature adults and larvae do not feed on larvae. In the above model. the cannibalism of larvae and callows by adults and of pupae and callows by larvae is assumed negligible since it typically occurs at much reduced rates. The constants J.11 and J.1a are the larval and adult probability of