Reactivity in prey–predator models at equilibrium under selective harvesting efforts

Abstract

Reactivity is an important feature of every stable state to measure the short-term instability of such stable state in prey–predator models. Asymptotic stability is not a powerful tool to study the dynamics immediately after an equilibrium has disturbed. We are interested in studying the effect of disturbance made by harvesting effort to the stable state of a set of prey–predator models. We consider different scenarios of disturbance made by prey harvesting only, predator harvesting only and selective harvesting on both. We show that disturbance made by prey harvesting causes reactivity of stable state but not in a sustainable way (non-existence of maximum sustainable yield). Further, it is shown that disturbance made by predator harvesting causes reactivity of stable state but in a sustainable way. We study how disturbance made by different harvesting strategies to the asymptotically stable state in the prey–predator system where intraspecific competition rule applied to predator species affects transient dynamics. We find that the transient dynamics properties like reactivity and non-reactivity switch through disturbance made by harvesting but in a sustainable way (maximum sustainable yield exists). Further, we find that asymptotically stable state remains reactive following multiple disturbances made by selective harvesting on both but in a sustainable way (maximum sustainable total yield exists)