IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v206y2023icp780-795.html
   My bibliography  Save this article

Thresholds and critical states for a stochastic predator–prey model with mixed functional responses

Author

Listed:
  • Zou, Xiaoling
  • Li, Qingwei
  • Cao, Wenhao
  • Lv, Jingliang

Abstract

In this paper, we are committed to the study of thresholds (between persistence and extinction) for all the species in a stochastic predator–prey model, which takes both Beddington–DeAngelis and Holling-II functional responses. One interesting thing we find is that the ith Lyapunov exponent defined for an ergodic invariant measure may just happen to be the threshold for the ith species. Furthermore, we discuss the priority levels among multiple thresholds for the same species, which is a novel feature of this paper. A brief summary of priority level is that, Lyapunov exponent for a high-dimensional measure has higher priority than that of a low-dimensional measure. At the end of the paper, we analyze dynamic properties for some critical states.

Suggested Citation

  • Zou, Xiaoling & Li, Qingwei & Cao, Wenhao & Lv, Jingliang, 2023. "Thresholds and critical states for a stochastic predator–prey model with mixed functional responses," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 780-795.
    • Handle: RePEc:eee:matcom:v:206:y:2023:i:c:p:780-795
    DOI: 10.1016/j.matcom.2022.12.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475422005031
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2022.12.016?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Hunki Baek & Dongseok Kim, 2014. "Dynamics of a Predator-Prey System with Mixed Functional Responses," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-10, September.
    2. Rihan, F.A. & Rajivganthi, C, 2020. "Dynamics of fractional-order delay differential model of prey-predator system with Holling-type III and infection among predators," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    3. Guo, Hongjian & Song, Xinyu, 2008. "An impulsive predator–prey system with modified Leslie–Gower and Holling type II schemes," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1320-1331.
    4. Rudnicki, Ryszard, 2003. "Long-time behaviour of a stochastic prey-predator model," Stochastic Processes and their Applications, Elsevier, vol. 108(1), pages 93-107, November.
    5. Zou, Xiaoling & Ma, Pengyu & Zhang, Liren & Lv, Jingliang, 2022. "Dynamic properties for a stochastic food chain model," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lan, Guijie & Chen, Zhewen & Wei, Chunjin & Zhang, Shuwen, 2018. "Stationary distribution of a stochastic SIQR epidemic model with saturated incidence and degenerate diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 511(C), pages 61-77.
    2. Huang, Zaitang, 2017. "Positive recurrent of stochastic coral reefs model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 751-761.
    3. Fu, Xiaoming, 2019. "On invariant measures and the asymptotic behavior of a stochastic delayed SIRS epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1008-1023.
    4. Guo, Xiaoxia & Zhu, Chunjuan & Ruan, Dehao, 2019. "Dynamic behaviors of a predator–prey model perturbed by a complex type of noises," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1024-1037.
    5. Ji, Chunyan & Jiang, Daqing & Lei, Dongxia, 2019. "Dynamical behavior of a one predator and two independent preys system with stochastic perturbations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 649-664.
    6. Alsakaji, Hebatallah J. & Kundu, Soumen & Rihan, Fathalla A., 2021. "Delay differential model of one-predator two-prey system with Monod-Haldane and holling type II functional responses," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    7. Settati, A. & Lahrouz, A. & Zahri, M. & Tridane, A. & El Fatini, M. & El Mahjour, H. & Seaid, M., 2021. "A stochastic threshold to predict extinction and persistence of an epidemic SIRS system with a general incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    8. Zhang, Xinhong & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2017. "Dynamical behavior of a stochastic SVIR epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 483(C), pages 94-108.
    9. Yang, Jiangtao, 2020. "Threshold behavior in a stochastic predator–prey model with general functional response," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    10. Muhammad Imran Liaqat & Ali Akgül & Hanaa Abu-Zinadah, 2023. "Analytical Investigation of Some Time-Fractional Black–Scholes Models by the Aboodh Residual Power Series Method," Mathematics, MDPI, vol. 11(2), pages 1-19, January.
    11. Chen, Xingzhi & Tian, Baodan & Xu, Xin & Zhang, Hailan & Li, Dong, 2023. "A stochastic predator–prey system with modified LG-Holling type II functional response," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 449-485.
    12. Liu, Qun & Jiang, Daqing & He, Xiuli & Hayat, Tasawar & Alsaedi, Ahmed, 2019. "Stationary distribution of a stochastic predator–prey model with distributed delay and general functional response," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 273-287.
    13. Cao, Boqiang & Shan, Meijing & Zhang, Qimin & Wang, Weiming, 2017. "A stochastic SIS epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 127-143.
    14. Zhang, Qiumei & Jiang, Daqing, 2021. "Dynamics of stochastic predator-prey systems with continuous time delay," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    15. Vadillo, Fernando, 2019. "Comparing stochastic Lotka–Volterra predator-prey models," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 181-189.
    16. Zuo, Wenjie & Jiang, Daqing & Sun, Xinguo & Hayat, Tasawar & Alsaedi, Ahmed, 2018. "Long-time behaviors of a stochastic cooperative Lotka–Volterra system with distributed delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 542-559.
    17. El Fatini, Mohamed & El Khalifi, Mohamed & Gerlach, Richard & Laaribi, Aziz & Taki, Regragui, 2019. "Stationary distribution and threshold dynamics of a stochastic SIRS model with a general incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    18. Wen, Buyu & Rifhat, Ramziya & Teng, Zhidong, 2019. "The stationary distribution in a stochastic SIS epidemic model with general nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 258-271.
    19. Sun, Xinguo & Zuo, Wenjie & Jiang, Daqing & Hayat, Tasawar, 2018. "Unique stationary distribution and ergodicity of a stochastic Logistic model with distributed delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 864-881.
    20. Zhang, Xinhong & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2017. "Dynamics of a stochastic SIS model with double epidemic diseases driven by Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 767-777.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:206:y:2023:i:c:p:780-795. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.