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Synchronization of Epidemic Systems with Neumann Boundary Value under Delayed Impulse

Author

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  • Ruofeng Rao

    (Department of Mathematics, Chengdu Normal University, Chengdu 611130, China)

  • Zhi Lin

    (Department of Mathematics, Chengdu Normal University, Chengdu 611130, China
    School of Mathematical and Computational Science, Hunan University of Science and Technology, Xiangtan 411201, China)

  • Xiaoquan Ai

    (Department of Mathematics, Chengdu Normal University, Chengdu 611130, China)

  • Jiarui Wu

    (Department of Mathematics, Chengdu Normal University, Chengdu 611130, China)

Abstract

This paper reports the construction of synchronization criteria for the delayed impulsive epidemic models with reaction–diffusion under the Neumann boundary value. Different from the previous literature, the reaction–diffusion epidemic model with a delayed impulse brings mathematical difficulties to this paper. In fact, due to the existence of second-order partial derivatives in the reaction–diffusion model with a delayed impulse, the methods of first-order ordinary differential equations from the previous literature cannot be effectively applied in this paper. However, with the help of the variational method and an appropriate boundedness assumption, a new synchronization criterion is derived, and its effectiveness is illustrated by numerical examples.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:2064-:d:839182
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    References listed on IDEAS

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    Cited by:

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    9. Hongguang Fan & Jiahui Tang & Kaibo Shi & Yi Zhao & Hui Wen, 2023. "Delayed Impulsive Control for μ -Synchronization of Nonlinear Multi-Weighted Complex Networks with Uncertain Parameter Perturbation and Unbounded Delays," Mathematics, MDPI, vol. 11(1), pages 1-17, January.
    10. Sergey Kashchenko, 2023. "Van der Pol Equation with a Large Feedback Delay," Mathematics, MDPI, vol. 11(6), pages 1-19, March.
    11. Natalya O. Sedova & Olga V. Druzhinina, 2023. "Exponential Stability of Nonlinear Time-Varying Delay Differential Equations via Lyapunov–Razumikhin Technique," Mathematics, MDPI, vol. 11(4), pages 1-15, February.
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    13. 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.
    14. 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.
    15. Li, Jing & Zhu, Quanxin, 2023. "Event-triggered impulsive control of stochastic functional differential systems," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    16. Alexandra Kashchenko, 2022. "Asymptotics of Solutions to a Differential Equation with Delay and Nonlinearity Having Simple Behaviour at Infinity," Mathematics, MDPI, vol. 10(18), pages 1-16, September.
    17. Yong Tang, 2023. "Traveling Wave Optical Solutions for the Generalized Fractional Kundu–Mukherjee–Naskar (gFKMN) Model," Mathematics, MDPI, vol. 11(11), pages 1-12, June.
    18. 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.
    19. Haiqing Du & Xiaojing Wang & Bo Du, 2023. "Positive Periodic Solution for Pipe/Tank Flow Configurations with Friction," Mathematics, MDPI, vol. 11(8), pages 1-11, April.
    20. Mahtab Mehrabbeik & Atefeh Ahmadi & Fatemeh Bakouie & Amir Homayoun Jafari & Sajad Jafari & Dibakar Ghosh, 2023. "The Impact of Higher-Order Interactions on the Synchronization of Hindmarsh–Rose Neuron Maps under Different Coupling Functions," Mathematics, MDPI, vol. 11(13), pages 1-18, June.
    21. Chengqiang Wang & Xiangqing Zhao & Can Wang & Zhiwei Lv, 2023. "Synchronization of Takagi–Sugeno Fuzzy Time-Delayed Stochastic Bidirectional Associative Memory Neural Networks Driven by Brownian Motion in Pre-Assigned Settling Time," Mathematics, MDPI, vol. 11(17), pages 1-32, August.
    22. Zhengqi Ma & Shoucheng Yuan & Kexin Meng & Shuli Mei, 2023. "Mean-Square Stability of Uncertain Delayed Stochastic Systems Driven by G-Brownian Motion," Mathematics, MDPI, vol. 11(10), pages 1-16, May.
    23. 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.
    24. Yong Tang & Lang Zhou & Jiahui Tang & Yue Rao & Hongguang Fan & Jihong Zhu, 2023. "Hybrid Impulsive Pinning Control for Mean Square Synchronization of Uncertain Multi-Link Complex Networks with Stochastic Characteristics and Hybrid Delays," Mathematics, MDPI, vol. 11(7), pages 1-18, April.

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