Analyse de la stabilité et diagnostic du chaos dans les systèmes dynamiques discrets avec applications.

Abstract

The objective of this work is to study discrete dynamical systems, introducing fundamental concepts such as stability, bifurcation, and chaos. We will then apply these concepts to a discrete-time predator-prey system with a Holling type-II functional response and prey refuge. Our study will analyze the stability and bifurcation of equilibrium points in this system. Finally, we will determine if this system exhibits chaotic behavior using Lyapunov exponents.