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Stability of Differential Systems with Impulsive Effects

Author

Listed:
  • Chunxiang Li

    (Department of Mathematics and Physics, Faculty of Military Medical Services, Naval Medical University, Shanghai 200433, China)

  • Fangshu Hui

    (Department of Mathematics and Physics, Faculty of Military Medical Services, Naval Medical University, Shanghai 200433, China)

  • Fangfei Li

    (School of Mathematics, East China University of Science and Technology, Shanghai 200237, China
    Key Laboratory of Smart Manufacturing in Energy Chemical Process, Ministry of Education, East China University of Science and Technology, Shanghai 200237, China)

Abstract

In this paper, a brief survey on the stability of differential systems with impulsive effects is provided. A large number of research results on the stability of differential systems with impulsive effects are considered. These systems include impulsive differential systems, stochastic impulsive differential systems and differential systems with several specific impulses (non-instantaneous impulses, delayed impulses, impulses suffered by logic choice and impulse time windows). The stability issues as well as the applications in neural networks are discussed in detail.

Suggested Citation

  • Chunxiang Li & Fangshu Hui & Fangfei Li, 2023. "Stability of Differential Systems with Impulsive Effects," Mathematics, MDPI, vol. 11(20), pages 1-23, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4382-:d:1264617
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    References listed on IDEAS

    as
    1. Huafei Chen & Jia Chen & Dan Qu & Kelin Li & Fei Luo, 2022. "An Uncertain Sandwich Impulsive Control System with Impulsive Time Windows," Mathematics, MDPI, vol. 10(24), pages 1-14, December.
    2. Shiguo Peng & Liping Yang, 2010. "Global Exponential Stability of Impulsive Functional Differential Equations via Razumikhin Technique," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-11, February.
    3. Pei Cheng & Fengqi Yao & Mingang Hua, 2014. "Stability Analysis of Impulsive Stochastic Functional Differential Equations with Delayed Impulses via Comparison Principle and Impulsive Delay Differential Inequality," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, February.
    4. Fengqi Yao & Feiqi Deng & Pei Cheng, 2013. "Exponential Stability of Impulsive Stochastic Functional Differential Systems with Delayed Impulses," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, April.
    5. Xiaodi Li & A. Vinodkumar & T. Senthilkumar, 2019. "Exponential Stability Results on Random and Fixed Time Impulsive Differential Systems with Infinite Delay," Mathematics, MDPI, vol. 7(9), pages 1-22, September.
    6. Chi Zhao & Yinfang Song & Quanxin Zhu & Kaibo Shi & Eric Campos, 2022. "Input-to-State Stability Analysis for Stochastic Mixed Time-Delayed Neural Networks with Hybrid Impulses," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-13, January.
    7. Jie Yang & Bing Xie, 2013. "New Results on Impulsive Functional Differential Equations with Infinite Delays," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, April.
    8. Pei Cheng & Zheng Wu & Lianglong Wang, 2012. "New Results on Global Exponential Stability of Impulsive Functional Differential Systems with Delayed Impulses," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-13, September.
    9. Kao, Yonggui & Zhu, Quanxin & Qi, Wenhai, 2015. "Exponential stability and instability of impulsive stochastic functional differential equations with Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 795-804.
    10. Li, Xiaodi & Shen, Jianhua & Rakkiyappan, R., 2018. "Persistent impulsive effects on stability of functional differential equations with finite or infinite delay," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 14-22.
    11. Liu, X. & Zeng, Y.M., 2019. "Analytic and numerical stability of delay differential equations with variable impulses," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 293-304.
    12. Fu, Xiaozheng & Zhu, Quanxin, 2020. "Exponential stability of neutral stochastic delay differential equation with delay-dependent impulses," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    13. Xiaotai Wu & Litan Yan & Wenbing Zhang & Liang Chen, 2012. "Exponential Stability of Impulsive Stochastic Delay Differential Systems," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-15, January.
    14. Yanke Du & Yanlu Li & Rui Xu, 2013. "Stability Analysis for Impulsive Stochastic Reaction-Diffusion Differential System and Its Application to Neural Networks," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-12, August.
    15. Zheng Wu & Hao Huang & Lianglong Wang, 2012. "Exponential Stability of Impulsive Stochastic Functional Differential Systems," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-12, May.
    16. X. Liu & Y. M. Zeng, 2017. "Stability Analysis of Analytical and Numerical Solutions to Nonlinear Delay Differential Equations with Variable Impulses," Discrete Dynamics in Nature and Society, Hindawi, vol. 2017, pages 1-8, November.
    17. Anju Sood & Sanjay K. Srivastava, 2015. "On Stability of Differential Systems with Noninstantaneous Impulses," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-5, April.
    18. Chunxiang Li & Lijuan Shen & Fangshu Hui & Wen Luo & Zhongliang Wang, 2023. "Mean Square Exponential Stability of Stochastic Delay Differential Systems with Logic Impulses," Mathematics, MDPI, vol. 11(7), pages 1-17, March.
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    1. Vitaly G. Il’ichev & Dmitry B. Rokhlin, 2023. "Paradoxes of Competition in Periodic Environments: Delta Functions in Ecological Models," Mathematics, MDPI, vol. 12(1), pages 1-12, December.

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