Journal
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
Volume 10, Issue 2, Pages 869-880Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.nonrwa.2007.11.010
Keywords
Modified logistic map; No window; Hyper-chaos; Asymptotic synchronization; Secure communication; Poincare recurrences
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Funding
- National Science Council
- National Center for Theoretical Sciences, Taiwan
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In this paper, we propose a Modified Logistic Map (MLM) and give a theoretical proof to show that the MLM is a chaotic map according to Devaney's definition. The MLM not only has no chaotic window but is also uniformly distributed in [0, 1] for gamma >= 4. Furthermore, on the basis of the MLMs, we establish a Modified Logistic Hyper-Chaotic System (MLHCS) and apply the MLHCS to develop a symmetric cryptography algorithm, Asymptotic Synchronization of the Modified Logistic Hyper-Chaotic System (ASMLHCS). In our numerical simulation, we analyze the spectra of waveforms of sequences generated from the MLM, showing that the orbit forms a uniform distribution in [0, 1]. In addition, we compute the Poincare recurrences which indicate that the MLM possesses a positive topological entropy. (C) 2007 Elsevier Ltd. All rights reserved.
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