Affiliation:
1. School of Business and Economics, The Arctic University of Norway-Campus, Harstad, Tromsø, Norway
Abstract
Two stage-structuredone-population (prey) models together with four prey-predator models are analyzed. Regarding the prey models, where one of them has fecundity elements which depend on the total population while the fecundities of the other depend on the mature part of the population only, we prove that both of them are permanent and moreover that their fixed points undergo supercritical bifurcations, flip, and Neimark-Sacker, respectively, at the various instability thresholds. By use of the models, we also provide a discussion of stability and dynamical properties of species who possess different life histories and extent results obtained elsewhere. Turning to predation, in contrast to what one finds in most papers, we scrutinize cases where both the immature subpopulation of the prey and the mature part are targets for the predator. Among our findings, here is that increased predation may act in both a stabilizing and destabilizing fashion depending on the size of fecundity of prey. Moreover, we present new results about the transition from stability to instability, and we show that whenever predation acts destabilizing, the effect is most profound in cases where the prey possesses a precocious semelparous life history. We also provide several examples where increased predation may turn a stable system chaotic.