Browsing by Author "Chang, Shu-Ming"

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Applying snapback repellers in resource budget models
(2011-12-01)
Chang, Shu-Ming
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Chen, Hsun-Hui
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應用數學系
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Department of Applied Mathematics
In Satake's generalized resource budget model of ecology, which was modified from Isagi's resource budget model, Satake and Iwasa illustrated, by computing the positive Lyapunov exponent, that if the depletion coefficient is greater than one, then the system is chaotic. However, a positive Lyapunov exponent implies only sensitivity in Devaney's chaos. Therefore, this work presents mathematical viewpoints and numerical analysis on Satake's generalized resource budget model to rigorously prove that the generalized resource budget model is chaotic in Devaney's sense by using the snapback repeller theory and the topological entropy theory. Moreover, this work also investigates that there is a significant difference between the behaviors of positive odd depletion coefficients and positive even depletion coefficients under numerical computations. (C) 2011 American Institute of Physics. [doi:10.1063/1.3660662]
Asymptotic synchronization of modified logistic hyper-chaotic systems and its applications
(2009-04-01)
Chang, Shu-Ming
;
Li, Ming-Chia
;
Lin, Wen-Wei
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應用數學系
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Department of Applied Mathematics
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.
Chaotic Generator in Digital Secure Communication
(2009)
Chang, Shu-Ming
;
應用數學系
;
Department of Applied Mathematics
A chaotic orbit generated by a nonlinear system is irregular, aperiodic, unpredictable and has sensitive: dependence oil initial conditions. However, the chaotic trajectory is still not well enough to be a crypto system in digital secure communication. Therefore, we propose a Modified Logistic Map (MLM) and give a theoretical proof to show that the MLM is a chaotic snap according to Devaney's definition. Based on the MLMs, we establish a Modified Logistic Hyper-Chaotic System (MLHCS) and apply MLHCS to develop a symmetric cryptography algorithm, Asymptotic Synchronization of Modified Logistic Hyper-Chaotic System (ASMLHCS).