Bistability and Bifurcations in Modified Nicholson-Bailey Model with Age-Structure for Prey

Abstract

The paper investigates dynamic modes of the predator-prey model with age structure for prey. We use a slight modification of the Nicholson-Bailey model to describe the interaction between predator and prey. We assume the population size is regulated by decreasing juvenile survival rate with growth of age class sizes. Conditions for sustainable coexistence of interacting species are described. It is shown that the coexistence of species becomes possible if there are a transcritical or saddle-node (tangential) bifurcations. Due to the saddle-node bifurcation there is bistability in the system of interacting species: predator either coexists with prey or dies depending on the initial conditions. It is shown that the range of demographic parameters, for which the prey and predator coexist, can significantly increase with growth of survival of adult prey or the proportion of predators born or the prey consumption rate of the predator. We studied the oscillation scenarios of interacting population, influences of reproduction, survival and self-regulation rates of population prey and age-dependent predation as well as variations in the current number on transitions between different dynamic modes. It is shown that an increase in the birth rate of the prey under intraspecific competition can lead to a dynamics destabilization and to oscillations appearance in numbers. Age-dependent predation is shown to be a stabilizing influence. At the same time, with a high birth rate of the prey, the system stability is ensured by the high survival rate of adult prey. It was found that in the model parametric space, both bistability and multistability arises, which are not related to each other. Consequently, even a small variation of the current population size leads to more complex behavior of the interacting species, and can give a significant change in both the observed dynamic mode and the coexistence scenario of the species.