Distributional chaos in a sequence and topologically weak mixing for nonautonomous discrete dynamical systems

Zhao, Yu; Li, Risong; Wang, Hongqing; Liang, Haihua

doi:10.22436/jmcs.020.01.02

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J. Math. Computer Sci.

2019

DOI: 10.22436/jmcs.020.01.02

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Distributional chaos in a sequence and topologically weak mixing for nonautonomous discrete dynamical systems

Yu Zhao¹,

Risong Li²,

Hongqing Wang³

et al.

Abstract: Assume that (W, g 1,∞) is a nonautonomous discrete dynamical system given by sequences (g m) ∞ m=1 of continuous maps on the space (W, d). In this paper, it is proven that if g 1,∞ is topologically weakly mixing and satisfies that g n 1 • g m 1 = g n+m 1 for any n, m ∈ {0, 1,. . .}, then it is distributional chaos in a sequence. This result extends the existing one.

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Improved Feature Selection Based on Chaos Game Optimization for Social Internet of Things with a Novel Deep Learning Model

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The Social Internet of Things (SIoT) ecosystem tends to process and analyze extensive data generated by users from both social networks and Internet of Things (IoT) systems and derives knowledge and diagnoses from all connected objects. To overcome many challenges in the SIoT system, such as big data management, analysis, and reporting, robust algorithms should be proposed and validated. Thus, in this work, we propose a framework to tackle the high dimensionality of transferred data over the SIoT system and improve the performance of several applications with different data types. The proposed framework comprises two parts: Transformer CNN (TransCNN), a deep learning model for feature extraction, and the Chaos Game Optimization (CGO) algorithm for feature selection. To validate the framework’s effectiveness, several datasets with different data types were selected, and various experiments were conducted compared to other methods. The results showed that the efficiency of the developed method is better than other models according to the performance metrics in the SIoT environment. In addition, the average of the developed method based on the accuracy, sensitivity, specificity, number of selected features, and fitness value is 88.30%, 87.20%, 92.94%, 44.375, and 0.1082, respectively. The mean rank obtained using the Friedman test is the best value overall for the competitive algorithms.

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Improved Feature Selection Based on Chaos Game Optimization for Social Internet of Things with a Novel Deep Learning Model

et al. 2023

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Distributional chaos in a sequence and topologically weak mixing for nonautonomous discrete dynamical systems

Cited by 1 publication

References 23 publications

Improved Feature Selection Based on Chaos Game Optimization for Social Internet of Things with a Novel Deep Learning Model

Improved Feature Selection Based on Chaos Game Optimization for Social Internet of Things with a Novel Deep Learning Model

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