Nonlinear analysis and chaos have many applications in communications, cryptography, and many other fields. In this work, we aim to bridge the gap between mathematical analysis of generalized 1D 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 z = xy in a general map that could yield each of them and other new maps. 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. © 2015 IEEE.
Sayed W.S., Hussien A.-L.E., Fahmy H.A.H., Radwan A.G.
Digital arithmetic; Lyapunov methods; Nonlinear analysis; Applications in communications; Digital platforms; Discrete chaotic maps; Elementary function; Finite precision; Floating point implementation; Mathematical analysis; Power functions; Chaotic systems
Proceedings of the IEEE International Conference on Electronics, Circuits, and Systems, Vol. 2016-March, Art. No. 7440363, PP. 506 to 507, Doi: 10.1109/ICECS.2015.7440363