Analyse dynamique et numérique d’un système non linéaire chaotique.

Abstract

This thesis provides an in-depth study of chaotic dynamic systems and their applications in the fields of cybersecurity and biological interactions. The study aims to exploit the properties of chaos to generate random numbers and apply them in modern encryption techniques, thereby enhancing the protection of digital data and secure communications, while also analyzing the impact of temporal scale variations on the stability of cological systems. In the field of cybersecurity, a model for image encryption has been studied using the Lorenz and Rössler systems to generate chaotic random integer numbers (CRINs), with the use of the XOR operation to achieve effective encryption. The thesis also includes the innovation of a system for encrypting and decrypting voice communications using a fourloop chaotic system, programmed in Python, which can be installed on multiple devices for secure communication, representing a significant advancement in communication security. In the field of biological interactions, the thesis focuses on studying the dynamics of ecosystems consisting of three trophic levels (prey - predator - super-predator). The impact of temporal scale variations on system stability was analyzed, showing that the presence of homoclinic orbits in the prey-predator subsystem leads to period doubling and the emergence of chaotic behavior in the overall system. This thesis combines both heoretical and applied aspects of chaotic systems, contributing to improving cybersecurity and providing a deeper understanding of biological phenomena.