Title: Effects of stage-structure on the dynamical output of a predator-prey model
Abstract: In [A.S. Ackleh, M.I. Hossain, A. Veprauskas, and A. Zhang, Persistence and stability analysis of discrete-time predator-prey models: A study of population and evolutionary dynamics, J. Differ. Equ. Appl. 25 (2019), pp. 1568–1603.], we developed a discrete-time predator-prey model. The prey was assumed to grow according to a Beverton–Holt nonlinearity in the absence of the predator. The growth of the predator population having density-independent survival probability was assumed to be dependent on prey consumption, which is limited by the number of prey a predator can consume per unit of time. This model was later extended to a model that includes a stage-structured predator population in which the predator is classified according to two developmental stages: juveniles and adults and only the adult predators are capable of attacking and consuming the prey population. In addition, it is also assumed that the maturation period is such that all juvenile predators become adults after a one-time unit. In addition, the initial model is also extended to include the stage-structured for the prey population and unstructured predator population. This current model has a similar stage-structured form to the prey population as considered for the predator population in the second model where only juvenile prey is consumed by the predator population. We thoroughly investigate the various dynamical behaviors of all these discrete-time predator-prey models such as the existence and uniqueness of the extinction, predator-free, and interior equilibria as well as the local and global stability of the equilibria and the persistence of the systems. We provide numerical examples showing the various dynamical scenarios in support of the theoretical results. These numerical simulations show that introducing stage-structure into the predator population allows for complicated rich dynamics that are not possible when the predator is unstructured.