Introduction to impulsive differential equations and applications

• Grant number: 22/07899-8
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: September 01, 2022
• End date: December 31, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Marta Cilene Gadotti
• Grantee: Arthur Medeiros Barros
• Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil

Abstract

This project aims to introduce the basic concepts and results of Impulsive Differential Equations (EDI). That is, to state and prove the classical results on the existence of a solution, a continuation of the solution, and stability of impulsive systems of ordinary differential equations. Exemplify this theory through biological and/or ecological models, such as the prey-predator type. Introduce the concept of pre-fixed impulse through the Kruger-Thiemer Model which describes how a given drug is absorbed by the body. But we will focus especially on situations where the impulse instants are not known in advance. Finally, we will establish some contrasts between EDO and EDI.(AU)