Abstract: A two-dimensional model is analyzed. It reflects the dynamics occurring in discrete Lorenz model. Invariant sets are analytically detected and the parameter space is investigated in order to classify completely regions of existence of stable 2-cycles, and regions associated with chaotic behaviors. This paper describes complex dynamics of invariant sets and weak attractors according to Tsybulin and Yudovich idea. These sets are displayed by numerical simulations.
Keywords: Noninvertible map; invariant set; weak attractor; bifurcation; basin of attraction.