Chaos, stabilité et coexistence dans les systèmes dynamiques.

Abstract

The aim of the present work consists in a study of the equivalence of two chaotic dynamic systems and to examine and clarify the equivalence of the systems to the Lorenz system. For this purpose we had give several conditions for general forms of three-dimensional quadratic autonomous systems with two quadratic terms to be equivalent to the Lorenz system, as it has happened, for example, with the Chen and Lu systems that are particular cases of the Lorenz systme. By the results obtained in our work, we have distinguished three well-known systems equivalent to the Lorenz system.