Digitally generating true orbits of binary shift chaotic maps and their conjugates

In this paper, we propose the algorithms using this simple method for digitally implementing binary shift chaotic maps. These algorithms are suitable for both software and hardware solutions, and they are also applicable with any random number generator or a repeated bit sequence. According to the type of the random number generator, either true periodic orbits or true chaotic orbits of the map are obtained. Moreover, it is shown that, utilizing topological conjugacies, obtained true orbits of binary shift chaotic maps can be used to calculate true orbits of other maps such as logistic and Chebyshev maps which are normally subject to round-off and truncation errors. The hardware implementations of binary shift chaotic maps, logistic map and Chebyshev maps have been realized on a Field Programmable Gate Array (FPGA) platform using the proposed algorithms.