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Generalized chaotic maps and elementary functions between analysis and implementation / Wafaa Saber Abdelhalim Sayed ; Supervised Abdellatif E. Hussien , Hossam A. H. Fahmy , Ahmed G. Radwan

By: Contributor(s): Material type: TextTextLanguage: English Publication details: Cairo : Wafaa Saber Abdelhalim Sayed , 2015Description: 138 P. : plans ; 30cmOther title:
  • خرائط الفوضى العامة و الدوال الأولية بين التحليل و التنفيذ [Added title page title]
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  • Issued also as CD
Dissertation note: Thesis (M.Sc.) - Cairo University - Faculty of Engineering - Department of Mathematics and Physics Summary: In this thesis, we aim to bridge the gap between mathematical analysis of generalized one - dimensional discrete chaotic maps and their implementation on digital platforms. We propose several variations and generalizations on the logistic and tent maps and employ the power function in a general map that could yield each of them and other new maps. We present negative control parameter maps that provide wider alternating-sign output ranges which are controllable by scaling parameters. Moreover, the proposed general powering map is mathematically analyzed and verified for boundary cases. A transition map is presented that exhibits responses in the intermediate range from tent to logistic map. Finite precision logistic map is studied explaining the impact of finitude on its properties. In addition, floating-point implementations of the power function are tested on the occurrence of special values of the operands
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Item type Current library Home library Call number Copy number Status Date due Barcode
Thesis Thesis قاعة الرسائل الجامعية - الدور الاول المكتبة المركزبة الجديدة - جامعة القاهرة Cai01.13.10.M.Sc.2015.Wa.G (Browse shelf(Opens below)) Not for loan 01010110067847000
CD - Rom CD - Rom مخـــزن الرســائل الجـــامعية - البدروم المكتبة المركزبة الجديدة - جامعة القاهرة Cai01.13.10.M.Sc.2015.Wa.G (Browse shelf(Opens below)) 67847.CD Not for loan 01020110067847000

Thesis (M.Sc.) - Cairo University - Faculty of Engineering - Department of Mathematics and Physics

In this thesis, we aim to bridge the gap between mathematical analysis of generalized one - dimensional discrete chaotic maps and their implementation on digital platforms. We propose several variations and generalizations on the logistic and tent maps and employ the power function in a general map that could yield each of them and other new maps. We present negative control parameter maps that provide wider alternating-sign output ranges which are controllable by scaling parameters. Moreover, the proposed general powering map is mathematically analyzed and verified for boundary cases. A transition map is presented that exhibits responses in the intermediate range from tent to logistic map. Finite precision logistic map is studied explaining the impact of finitude on its properties. In addition, floating-point implementations of the power function are tested on the occurrence of special values of the operands

Issued also as CD

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