Aspects chaotiques dans les systèmes dynamiques discrets.

Abstract

A new modified 2-D discrete chaotic system with rational fraction is introduced in this thesis ; it has more complicated dynamical structures than HÈnon map and Lozi map. Some dynamical behaviors, Öxed points, period-doubling bifurcation, the way to chaos, and Lyapunov exponents spectrum, are further investigated using both theoretical analysis and numerical simulation. In particular, the map under consideration is a simple rational discrete bounded map capable of generating ìmulti- foldîstrange attractors via period-doubling bifurcation ways to chaos. This new discrete chaotic system has extensive application in many Öelds, such as optimization and secure communication