Applications in biology of piecewise differential equations

Abstract

Many phenomena in applied sciences can be modeled by using piecewise dynamic systems. Usually, the varieties of separation of the piecewise systems arise through abrupt changes in a determined system, e.g., in the refraction light, activation of neurons or electronic switches, when occurring collisions, taking decisions, and cell mitoses, or even through populations selectively moving between habitats or changes in their diet, or numerous other processes that enact a regime change in the system. In this project, we propose to study the relationship dynamics of bacteria in response to alternation in the feeding of the host (e.g., periods of fasting and different diets). Recently, was developed many approaches involving dynamic of bacteria considering the Lotka-Volterra System. Here we pretend to describe these processes through piecewise approaches, which makes it possible to find new insights into the manipulation of these microorganisms. However, we leave open the possibility of changing the application for another biological system of interest. (AU)