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Stability analysis of Nicholson’s blowflies equation with two different delays

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  • Huang, Chuangxia
  • Yang, Xiaoguang
  • Cao, Jinde

Abstract

This paper investigates an autonomous Nicholson’s blowflies equation incorporating two different delays. By using differential inequality techniques and dynamical system approaches, we establish two novel criteria to check the global exponential stability and asymptotical stability on the zero equilibrium point of the addressed equation, respectively. Our research partially answers an open question raised by Berezansky and Braverman (2017). A numerical example with simulations shows that the main theoretical results are correct.

Suggested Citation

  • Huang, Chuangxia & Yang, Xiaoguang & Cao, Jinde, 2020. "Stability analysis of Nicholson’s blowflies equation with two different delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 171(C), pages 201-206.
    • Handle: RePEc:eee:matcom:v:171:y:2020:i:c:p:201-206
    DOI: 10.1016/j.matcom.2019.09.023
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    References listed on IDEAS

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    1. Győri, István & Hartung, Ferenc & Mohamady, Nahed A., 2015. "On a nonlinear delay population model," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 909-925.
    2. Berezansky, Leonid & Braverman, Elena, 2016. "Boundedness and persistence of delay differential equations with mixed nonlinearity," Applied Mathematics and Computation, Elsevier, vol. 279(C), pages 154-169.
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    Cited by:

    1. Huang, Chuangxia & Liu, Bingwen & Qian, Chaofan & Cao, Jinde, 2021. "Stability on positive pseudo almost periodic solutions of HPDCNNs incorporating D operator," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 1150-1163.
    2. Junrong Guo & Xiaolin Liu & Ping Yan, 2023. "Dynamic Analysis of Impulsive Differential Chaotic System and Its Application in Image Encryption," Mathematics, MDPI, vol. 11(23), pages 1-18, November.
    3. Lingping Zhang & Bo Du, 2022. "Some New Existence Results for Positive Periodic Solutions to First-Order Neutral Differential Equations with Variable Coefficients," Mathematics, MDPI, vol. 10(20), pages 1-9, October.

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