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Generalized Halanay Inequalities and Relative Application to Time-Delay Dynamical Systems

Author

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  • Chunsheng Wang

    (Software Engineering Institute of Guangzhou, Guangzhou 510990, China
    Faculty of Finance, City University of Macau, Macau 999078, China
    School of Mathematical and Computational Science, Hunan University of Science and Technology, Xiangtan 411201, China)

  • Xiangdong Liu

    (School of Economics, Jinan University, Guangzhou 510632, China)

  • Feng Jiao

    (School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China)

  • Hong Mai

    (School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China)

  • Han Chen

    (School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen 518172, China)

  • Runpeng Lin

    (Software Engineering Institute of Guangzhou, Guangzhou 510990, China)

Abstract

A class of generalized Halanay inequalities is studied via the Banach fixed point method and comparison principle. The conditions to ensure the boundedness and stability of the zero solution are obtained in this study. This research provides a new approach to the study of the boundedness and stability of Halanay inequality. Numerical examples and simulation results verify the validity and superiority of the conclusions obtained in this study.

Suggested Citation

  • Chunsheng Wang & Xiangdong Liu & Feng Jiao & Hong Mai & Han Chen & Runpeng Lin, 2023. "Generalized Halanay Inequalities and Relative Application to Time-Delay Dynamical Systems," Mathematics, MDPI, vol. 11(8), pages 1-11, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1940-:d:1128341
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    References listed on IDEAS

    as
    1. Ruofeng Rao & Zhi Lin & Xiaoquan Ai & Jiarui Wu, 2022. "Synchronization of Epidemic Systems with Neumann Boundary Value under Delayed Impulse," Mathematics, MDPI, vol. 10(12), pages 1-10, June.
    2. Mingli Xia & Linna Liu & Jianyin Fang & Yicheng Zhang, 2023. "Stability Analysis for a Class of Stochastic Differential Equations with Impulses," Mathematics, MDPI, vol. 11(6), pages 1-10, March.
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    Cited by:

    1. Qing Yang & Xiaojing Wang & Xiwang Cheng & Bo Du & Yuxiao Zhao, 2023. "Positive Periodic Solution for Neutral-Type Integral Differential Equation Arising in Epidemic Model," Mathematics, MDPI, vol. 11(12), pages 1-13, June.
    2. Wei Ouyang & Kui Mei, 2023. "A General Iterative Procedure for Solving Nonsmooth Constrained Generalized Equations," Mathematics, MDPI, vol. 11(22), pages 1-17, November.
    3. Chao Wang & Yinfang Song & Fengjiao Zhang & Yuxiao Zhao, 2023. "Exponential Stability of a Class of Neutral Inertial Neural Networks with Multi-Proportional Delays and Leakage Delays," Mathematics, MDPI, vol. 11(12), pages 1-14, June.
    4. Zhao Li & Chen Peng, 2023. "Dynamics and Embedded Solitons of Stochastic Quadratic and Cubic Nonlinear Susceptibilities with Multiplicative White Noise in the Itô Sense," Mathematics, MDPI, vol. 11(14), pages 1-11, July.
    5. Bahua Lin & Zhan Zhou, 2023. "Positive Solutions to the Discrete Boundary Value Problem of the Kirchhoff Type," Mathematics, MDPI, vol. 11(16), pages 1-14, August.

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