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