Asymptotic synchronization of modified logistic hyper-chaotic systems and its applications

Shu-Ming Chang, Ming-Chia Li, Wen-Wei Lin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


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 γ ≥ 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 Poincaré recurrences which indicate that the MLM possesses a positive topological entropy.

Original languageAmerican English
Pages (from-to)869-880
Number of pages12
JournalNonlinear Analysis: Real World Applications
Issue number2
StatePublished - 1 Apr 2009


  • Asymptotic synchronization
  • Hyper-chaos
  • Modified logistic map
  • No window
  • Poincaré recurrences
  • Secure communication


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