Attraction to equilibria in stage-structured predator prey models and bio-control problems. (English) Zbl 1411.92256
Summary: Controlling invasive species has become an important ecological issue over the last decades. A popular management strategy consists of releasing natural enemies, generally predators. From a mathematical point of view, the study of any realistic problem in bio-control normally involves models remarkably resistant to the analysis. In this paper, we propose a new iterative method for studying the dynamical behaviour of a predator-prey model in which an invasive plant is subject to predation of an insect population. We show that the dynamics of the model depends on a suitable scalar function that determines the existence of equilibria.
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