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Practical Exponential Stability of Impulsive Stochastic Food Chain System with Time-Varying Delays

Author

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  • Yuxiao Zhao

    (School of Mathematics and Information Science, Shandong Technology and Business University, Yantai 264005, China
    School of Mathematical and Computational Science, Hunan University of Science and Technology, Xiangtan 411201, China)

  • Linshan Wang

    (School of Mathematial Science, Ocean University of China, Qingdao 266100, China)

Abstract

This paper studies the practical exponential stability of an impulsive stochastic food chain system with time-varying delays (ISOFCSs). By constructing an auxiliary system equivalent to the original system and comparison theorem, the existence of global positive solutions to the suggested system is discussed. Moreover, we investigate the sufficient conditions for the exponential stability and practical exponential stability of the system, which is given by Razumikhin technique and the Lyapunov method. In addition, when Razumikhin’s condition holds, the exponential stability and practical exponential stability of species are independent of time delay. Finally, numerical simulation finds the validity of the method.

Suggested Citation

  • Yuxiao Zhao & Linshan Wang, 2022. "Practical Exponential Stability of Impulsive Stochastic Food Chain System with Time-Varying Delays," Mathematics, MDPI, vol. 11(1), pages 1-12, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2022:i:1:p:147-:d:1017746
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    References listed on IDEAS

    as
    1. Yuxiao Zhao & Linshan Wang & Yangfan Wang, 2021. "The Periodic Solutions to a Stochastic Two-Prey One-Predator Population Model with Impulsive Perturbations in a Polluted Environment," Methodology and Computing in Applied Probability, Springer, vol. 23(3), pages 859-872, September.
    2. Peng, Shige & Zhu, Xuehong, 2006. "Necessary and sufficient condition for comparison theorem of 1-dimensional stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 116(3), pages 370-380, March.
    3. Wu, Jian, 2018. "Stability of a three-species stochastic delay predator–prey system with Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 492-505.
    4. 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.
    5. Mao, Xuerong & Marion, Glenn & Renshaw, Eric, 2002. "Environmental Brownian noise suppresses explosions in population dynamics," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 95-110, January.
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    Cited by:

    1. Wang, Chen & Zhang, Hai & Ye, Renyu & Zhang, Weiwei & Zhang, Hongmei, 2023. "Finite time passivity analysis for Caputo fractional BAM reaction–diffusion delayed neural networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 424-443.

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