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Mathematical Problems in Engineering
Volume 2015, Article ID 121359, 12 pages
Research Article

A Generalized Stability Theorem for Discrete-Time Nonautonomous Chaos System with Applications

School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China

Received 17 April 2015; Accepted 7 July 2015

Academic Editor: Ricardo Aguilar-López

Copyright © 2015 Mei Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Firstly, this study introduces a definition of generalized stability (GST) in discrete-time nonautonomous chaos system (DNCS), which is an extension for chaos generalized synchronization. Secondly, a constructive theorem of DNCS has been proposed. As an example, a GST DNCS is constructed based on a novel 4-dimensional discrete chaotic map. Numerical simulations show that the dynamic behaviors of this map have chaotic attractor characteristics. As one application, we design a chaotic pseudorandom number generator (CPRNG) based on the GST DNCS. We use the SP800-22 test suite to test the randomness of four 100-key streams consisting of 1,000,000 bits generated by the CPRNG, the RC4 algorithm, the ZUC algorithm, and a 6-dimensional CGS-based CPRNG, respectively. The numerical results show that the randomness performances of the two CPRNGs are promising. In addition, theoretically the key space of the CPRNG is larger than 21116. As another application, this study designs a stream avalanche encryption scheme (SAES) in RGB image encryption. The results show that the GST DNCS is able to generate the avalanche effects which are similar to those generated via ideal CPRNGs.