Authors: Mohamed Réda Ferchichi; Abla Yousfi
Addresses: Laboratory of Mathematics, Dynamics and Modelization, University Badji Mokhtar, Annaba 23000, Algeria ' Laboratory of Mathematics, Dynamics and Modelization, University Badji Mokhtar, Annaba 23000, Algeria
Abstract: In this paper, we study the appearance, evolution and neighbourhood of two attractors of a dynamical system defined by a quadratic polynomial map T: R2 → R2. The first is a Cantor-type attractor located on an invariant straight line. Thus, it suffices to study the restriction of the map T to this invariant line. The second is a closed curves cycle of period 2. We show, by a numerical approach, that when a parameter of the system varies, the evolution of the orbits in the region close to this second attractor is dependent on the evolution of the stable and unstable sets (homoclinic tangency) of a saddle cycle of period 2 located in this region.
Keywords: discrete dynamical systems; attractors; cantor sets; invariant curves; saddle-node and homoclinic bifurcations.
International Journal of Dynamical Systems and Differential Equations, 2019 Vol.9 No.1, pp.87 - 103
Received: 14 Oct 2017
Accepted: 03 Nov 2017
Published online: 09 Mar 2019 *