A Study on the Dynamics of a Generalized Logistic Map

Kazuomi KUBOTA  Yoichi MAEDA  Kazuyuki AIHARA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E83-A   No.3   pp.524-531
Publication Date: 2000/03/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Nonlinear Problems
logistic map,  Schwarzian derivative,  bifurcation,  intermittent chaos,  

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Nonlinear dynamics of xn+1=λ {4xn (1-xn)}q is studied in this paper. Different from the logistic map (q=1), in the case of q<q1=(33-3)/12=0.22871, there exists subcritical bifurcation because the Schwarzian derivative cannot preserve its sign at the fixed point. Moreover, when q<q2=0.17585 and λ=1.0, a stable period 1 orbit appears due to stabilization of the non-zero fixed point. Intermittent chaos due to the type 3 of intermittency is also found in this system.