Systèmes dynamiques à temps discrets et applications en biologie

Abstract

In this work, we are interested in the study of discrete-time dynamical systems. We are present the results of theoretical and numerical study of a discrete-time chaotic systems. We begin our study by plotting attractors obtained by numerical methods. We analyze the stability of fixed points. This work has three main parts. In the first part we five a study of the theory of chaos for topological dynamical systems defined by discrete maps for example the theorem of Li and Yorke in the case of dimension 1, and Marotto’s theorem in the case of the dimension n and Devaney’s theorem. The second part concerns the mathematical modeling and numerical simulation of tumor growth. We propose the model of De Pillis and Radunskaya. In the third part we present some methods used for discretization of dynamical systems, for example Euler method, Taylor method and Runge-Kutta method and we study the model of De Pillis and Radunskaya in discrete-time and with the method of discretization of Euler.