Publication IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer SciencesVol.E83-ANo.3pp.524-531 Publication Date: 2000/03/25 Online ISSN: DOI: Print ISSN: 0916-8508 Type of Manuscript: PAPER Category: Nonlinear Problems Keyword: logistic map, Schwarzian derivative, bifurcation, intermittent chaos,

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Summary: Nonlinear dynamics of x_{n+1}=λ {4x_{n} (1-x_{n})}^{q} is studied in this paper. Different from the logistic map (q=1), in the case of q<q_{1}=(33-3)/12=0.22871, there exists subcritical bifurcation because the Schwarzian derivative cannot preserve its sign at the fixed point. Moreover, when q<q_{2}=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.