Dynamical systems and biomathematics

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.