The chaotic dynamics of high-dimensional systems

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• 作者：Marjan Abdechiri ; Karim Faez ; Hamidreza Amindavar ; Eleonora Bilotta
• 关键词：Chaotic time series ; Compressive sensing ; Nonlinear system ; Fractal theory ; Image compression
• 刊名：Nonlinear Dynamics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：87
• 期：4
• 页码：2597-2610
• 全文大小：
• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems, Control; Classical Mechanics; Mechanical Engineering; Automotive Engineering;
• 出版者：Springer Netherlands
• ISSN：1573-269X
• 卷排序：87

文摘

This paper introduced a new method to exploit chaotic, sparse representations of nonlinear time series data. The methodology of the algorithm included two steps. First, the proposed method applied the fractal theory to estimate optimal dimension in a compressive sensing of a time series, and sparse data were concentrated on a pseudo-orbit trajectory. Second, the chaotic trajectory was extracted from the data obtained from the first step by employing a chaos prediction method. To verify the efficiency of the proposed method, the algorithm is applied to three categories, consisting of chaotic noise reduction, signal compression, and image compression. The experimental results indicated that the proposed method outperformed other state-of-the-art methods with up to a 95% reduction in errors. Moreover, the results demonstrated that sparse, chaotic representation was most effective in signal and image compression.