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Mean Li-Yorke Chaos and Mean Sensitivity in Non-autonomous Discrete Systems

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Abstract

In this paper, mean Li-Yorke chaos and mean sensitivity are investigated in non-autonomous discrete systems \((X, f_{1, \infty })\), where \(f_{1, \infty } = \{f_{i}\}_{i \geq 1}\) is a sequence of self-maps on a metric space X. It is shown that mean Li-Yorke chaos is preserved under iteration for a non-autonomous discrete system with certain continuity. Moreover, sensitivity, Banach mean sensitivity and mean sensitivity of non-autonomous linear discrete systems are characterized, respectively. We provide sufficient conditions under which a mean sensitive non-autonomous discrete system is mean Li-Yorke chaotic.

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Acknowledgements

The authors would like to express their gratitude to the anonymous referees for their valuable comments and suggestions.

Funding

This work was partly supported by the National Natural Science Foundation of China (No. 11701584, 11801096, 12101415) and Natural Science Research Project of Guangdong Province (No. 2017KQNCX122).

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Authors and Affiliations

  1. School of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou, 510665, People’s Republic of China

    Zongbin Yin & Zhijing Chen

  2. College of Mathematics and Statistics, Shenzhen University, Shenzhen, 518060, People’s Republic of China

    Shengnan He

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  1. Zongbin Yin
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  2. Shengnan He
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  3. Zhijing Chen
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Correspondence to Zongbin Yin.

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Yin, Z., He, S. & Chen, Z. Mean Li-Yorke Chaos and Mean Sensitivity in Non-autonomous Discrete Systems. J Dyn Control Syst 29, 245–262 (2023). https://doi.org/10.1007/s10883-022-09599-w

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  • DOI: https://doi.org/10.1007/s10883-022-09599-w

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