IDEAS home Printed from https://ideas.repec.org/a/wly/jnljam/v2014y2014i1n536019.html

Dynamics of a Predator‐Prey System with Mixed Functional Responses

Author

Listed:
  • Hunki Baek
  • Dongseok Kim

Abstract

A predator‐prey system with two preys and one predator is considered. Especially, two different types of functional responses, Holling type and Beddington‐DeAngelis type, are adopted. First, the boundedness of system is showed. Stabilities analysis of system is investigated via some properties about equilibrium points and stabilities of two subsystems without one of the preys of system. Also, persistence conditions of system are found out and some numerical examples are illustrated to substantiate our theoretical results.

Suggested Citation

  • Hunki Baek & Dongseok Kim, 2014. "Dynamics of a Predator‐Prey System with Mixed Functional Responses," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:536019
    DOI: 10.1155/2014/536019
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2014/536019
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2014/536019?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
    ---><---

    References listed on IDEAS

    as
    1. Lv, Songjuan & Zhao, Min, 2008. "The dynamic complexity of a three species food chain model," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1469-1480.
    2. Naji, Raid Kamel & Balasim, Alla Tariq, 2007. "Dynamical behavior of a three species food chain model with Beddington–DeAngelis functional response," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1853-1866.
    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. Zhao, Min & Lv, Songjuan, 2009. "Chaos in a three-species food chain model with a Beddington–DeAngelis functional response," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2305-2316.
    2. Singh, Anuraj & Gakkhar, Sunita, 2015. "Controlling chaos in a food chain model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 115(C), pages 24-36.
    3. Dai, Chuanjun & Zhao, Min & Chen, Lansun, 2012. "Complex dynamic behavior of three-species ecological model with impulse perturbations and seasonal disturbances," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 84(C), pages 83-97.
    4. Gupta, R.P. & Yadav, Dinesh K., 2023. "Nonlinear dynamics of a stage-structured interacting population model with honest signals and cues," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    5. Dahlia Khaled Bahlool & Huda Abdul Satar & Hiba Abdullah Ibrahim, 2020. "Order and Chaos in a Prey‐Predator Model Incorporating Refuge, Disease, and Harvesting," Journal of Applied Mathematics, John Wiley & Sons, vol. 2020(1).
    6. Younghae Do & Hunki Baek & Yongdo Lim & Dongkyu Lim, 2011. "A Three‐Species Food Chain System with Two Types of Functional Responses," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    7. Zhao, Tiantian & Han, Xiaoling, 2025. "Complex dynamics of Hastings–Powell model with additive Allee effect and Crowley–Martin functional response," Chaos, Solitons & Fractals, Elsevier, vol. 198(C).
    8. Yu, Hengguo & Zhong, Shouming & Ye, Mao, 2009. "Dynamic analysis of an ecological model with impulsive control strategy and distributed time delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(3), pages 619-632.
    9. Florencia Carusela, M. & Momo, Fernando R. & Romanelli, Lilia, 2009. "Competition, predation and coexistence in a three trophic system," Ecological Modelling, Elsevier, vol. 220(19), pages 2349-2352.
    10. Ali, Emad & Asif, Mohammed & Ajbar, AbdelHamid, 2013. "Study of chaotic behavior in predator–prey interactions in a chemostat," Ecological Modelling, Elsevier, vol. 259(C), pages 10-15.
    11. Wu, Yuhang & Ni, Mingkang, 2024. "Complex dynamics in a singularly perturbed Hastings–Powell model with the additive Allee effect," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    12. Lv, Songjuan & Fang, Zhongmiao, 2009. "The dynamic complexity of a host–parasitoid model with a Beddington–DeAngelis functional response," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2617-2623.
    13. Xinhong Pan & Min Zhao & Chuanjun Dai & Yapei Wang, 2015. "Dynamic Analysis of a Delayed Reaction‐Diffusion Predator‐Prey System with Modified Holling‐Tanner Functional Response," Abstract and Applied Analysis, John Wiley & Sons, vol. 2015(1).
    14. Min Zhao & Chuanjun Dai, 2014. "Nonlinear Dynamic in an Ecological System with Impulsive Effect and Optimal Foraging," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    15. Jin Yang & Min Zhao, 2012. "A Mathematical Model for the Dynamics of a Fish Algae Consumption Model with Impulsive Control Strategy," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    16. Zhang, Limin & Zhao, Min, 2009. "Dynamic complexities in a hyperparasitic system with prolonged diapause for host," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1136-1142.
    17. Zhu, Lili & Zhao, Min, 2009. "Dynamic complexity of a host–parasitoid ecological model with the Hassell growth function for the host," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1259-1269.
    18. Cai, Liming & Li, Xuezhi & Yu, Jingyuan & Zhu, Guangtian, 2009. "Dynamics of a nonautonomous predator–prey dispersion–delay system with Beddington–DeAngelis functional response," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 2064-2075.
    19. Zhao, Min & Wang, Xitao & Yu, Hengguo & Zhu, Jun, 2012. "Dynamics of an ecological model with impulsive control strategy and distributed time delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(8), pages 1432-1444.
    20. Raw, S.N. & Mishra, P. & Kumar, R. & Thakur, S., 2017. "Complex behavior of prey-predator system exhibiting group defense: A mathematical modeling study," Chaos, Solitons & Fractals, Elsevier, vol. 100(C), pages 74-90.

    More about this item

    Statistics

    Access and download statistics

    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:wly:jnljam:v:2014:y:2014:i:1:n:536019. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4185 .

    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.