Dynamical systems and biomathematics

• Grant number: 15/06942-3
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: June 01, 2015
• End date: May 31, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Maurício Richartz
• Grantee: Maria Clara Assay Sarem
• Host Institution: Centro de Matemática, Computação e Cognição (CMCC). Universidade Federal do ABC (UFABC). Ministério da Educação (Brasil). Santo André , SP, Brazil

Abstract

We propose an introduction to the broad and complex area of Dynamical Systems, with emphasis on biomathematical applications. The research plan starts with a study of ordinary differential equations which complements regular undergraduate courses. Next, a systematic study of Dynamical Systems will be conducted, starting with first-order equations, followed by phase space and periodic orbits, and ending with chaos. In the second stage of the project, several biological applications will be analyzed, including, but not limited to, discrete and continuous populational models, interaction species models (prey-predator), dynamics of marital interaction, and reaction kinetics. It is important to remark that all mathematical analysis of the project will be complemented by plots and simulations made with Scilab.