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Dynamic Analysis of a Pest Management Smith Model with Impulsive State Feedback Control and Continuous Delay

Author

Listed:
  • Zhenzhen Shi

    (College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China)

  • Yaning Li

    (College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China)

  • Huidong Cheng

    (College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China)

Abstract

In our paper, we propose a single population Smith model with continuous delay and impulsive state feedback control. The application in pest management of this model is investigated. First, the singularity of this model is qualitatively analyzed; then, we consider the existence and uniqueness of order-one periodic orbit in order to determine the frequency of the implementation of chemical control. Moreover, based on the limit method of the sequences of subsequent points, we verify the stability of periodic orbit to ensure a certain robustness of this control; at last, we carry out the numerical simulations to verify the correctness of the theoretical results.

Suggested Citation

  • Zhenzhen Shi & Yaning Li & Huidong Cheng, 2019. "Dynamic Analysis of a Pest Management Smith Model with Impulsive State Feedback Control and Continuous Delay," Mathematics, MDPI, vol. 7(7), pages 1-15, July.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:7:p:591-:d:244774
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    References listed on IDEAS

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    1. Liu, Xia & Zhang, Tonghua & Meng, Xinzhu & Zhang, Tongqian, 2018. "Turing–Hopf bifurcations in a predator–prey model with herd behavior, quadratic mortality and prey-taxis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 446-460.
    2. Guodong Liu & Xiaohong Wang & Xinzhu Meng & Shujing Gao, 2017. "Extinction and Persistence in Mean of a Novel Delay Impulsive Stochastic Infected Predator-Prey System with Jumps," Complexity, Hindawi, vol. 2017, pages 1-15, June.
    3. Sun, Kaibiao & Zhang, Tonghua & Tian, Yuan, 2017. "Dynamics analysis and control optimization of a pest management predator–prey model with an integrated control strategy," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 253-271.
    4. Chang, Zhengbo & Meng, Xinzhu & Lu, Xiao, 2017. "Analysis of a novel stochastic SIRS epidemic model with two different saturated incidence rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 472(C), pages 103-116.
    5. Jiao, Jianjun & Yang, Xiaosong & Cai, Shaohong & Chen, Lansun, 2009. "Dynamical analysis of a delayed predator-prey model with impulsive diffusion between two patches," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(3), pages 522-532.
    6. Ghosh, Bapan & Grognard, Frédéric & Mailleret, Ludovic, 2015. "Natural enemies deployment in patchy environments for augmentative biological control," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 982-999.
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