Applications in biology of piecewise differential equations

• Grant number: 22/14484-9
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• Start date: January 01, 2023
• End date: December 31, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Principal Investigator: Regilene Delazari dos Santos Oliveira
• Grantee: Leonardo Pereira Costa da Cruz
• Supervisor: Josep Sardanyes
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Institution abroad: Centre de Recerca Matemàtica (CRM), Spain
• Associated to the scholarship: 21/14987-8 - Bifurcation of limit cycles in smooth piecewise systems and an application in Medicine, BP.PD

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)