Mathematical Modeling of Exponential Growth with Impulsive Perturbations and Applications in Ecology

Abstract

This paper studies the dynamics of any population growing in a bioreactor with instantaneous perturbations caused by taking away or adding a biomass at certain moments. The case when the perturbations are of negligible length is investigated, and impulsive differential equations are used for modeling the situation. The studied populations either grow or decay exponentially between two consecutive perturbations. Several different models depending on the type of perturbations are examined; for each model, existence results and explicit formulas for the solutions are obtained. Theoretical results are applied to several real-life cases to predict the population sizes in time, as well as the instant and the amount of the perturbations. We can find a means to control the considered ecosystem using the obtained results for the new models, and save

time and money for conducting experiments and measuring population size.

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