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

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≥4γ≥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.