Hopf-bifurcations on a Nonlinear Chaotic Discrete Model

Abstract: In this paper we highlight some analytical and numerical discussion of Hopf bifurcation for the nonlinear two-dimensional chaotic map in the plane 22:f given by),(),( 22 yxybxyxbxayxf where the adjustable parameters.,ba Here we firstly show that if the nonlinear map f undergoes supercritical Hopf bifurcation, then 2f undergoes subcritical Hopf bifurcation. Secondly, we show that our numerical and graphical investigations have established some fascinating observation between Hopf bifurcation and Period-doubling bifurcation