Archive
Volume 1, Issue 2
International Journal of Science and Engineering Applications (IJSEA)
Volume 1, Issue 2 - December 2012
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 
given by
where the adjustable parameters 
Here we firstly show that if the nonlinear map
undergoes supercritical Hopf bifurcation, then
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.
Keywords: Supercritical Hopf bifurcation / Subcritical Hopf bifurcation / Period-doubling bifurcation / Nonlinear / Chaotic. 2010 AMS Classification: 37 G 15, 37 G 35, 37 C 45
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