IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2014y2014i1n169609.html

Nonlinear Dynamic in an Ecological System with Impulsive Effect and Optimal Foraging

Author

Listed:
  • Min Zhao
  • Chuanjun Dai

Abstract

The population dynamics of a three‐species ecological system with impulsive effect are investigated. Using the theories of impulsive equations and small‐amplitude perturbation scales, the conditions for the system to be permanent when the number of predators released is less than some critical value can be obtained. Furthermore, because the predator in the system follows the predictions of optimal foraging theory, it follows that optimal foraging promotes species coexistence. In particular, the less beneficial prey can support the predator alone when the more beneficial prey goes extinct. Moreover, the influences of the impulsive effect and optimal foraging on inherent oscillations are studied using simulation, which reveals rich dynamic behaviors such as period‐halving bifurcations, a chaotic band, a periodic window, and chaotic crises. In addition, the largest Lyapunov exponent and the power spectra of the strange attractor, which can help analyze the chaotic dynamic behavior of the model, are investigated. This information will be useful for studying the dynamic complexity of ecosystems.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:169609
    DOI: 10.1155/2014/169609
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2014/169609
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2014/169609?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. 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.
    2. Hai-Feng Huo & Zhan-Ping Ma & Chun-Ying Liu, 2009. "Persistence and Stability for a Generalized Leslie-Gower Model with Stage Structure and Dispersal," Abstract and Applied Analysis, Hindawi, vol. 2009, pages 1-17, July.
    3. Jinhuo Luo, 2010. "Permanence and Extinction of a Generalized Gause-Type Predator-Prey System with Periodic Coefficients," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-24, January.
    4. Hai-Feng Huo & Zhan-Ping Ma & Chun-Ying Liu, 2009. "Persistence and Stability for a Generalized Leslie‐Gower Model with Stage Structure and Dispersal," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).
    5. Upadhyay, Ranjit Kumar & Naji, Raid Kamel, 2009. "Dynamics of a three species food chain model with Crowley–Martin type functional response," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1337-1346.
    6. 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.
    7. Jinhuo Luo, 2010. "Permanence and Extinction of a Generalized Gause‐Type Predator‐Prey System with Periodic Coefficients," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    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. 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.
    2. 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.
    3. 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.
    4. Zhang, Limin & Zhang, Chaofeng & Zhao, Min, 2014. "Dynamic complexities in a discrete predator–prey system with lower critical point for the prey," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 105(C), pages 119-131.
    5. 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).
    6. 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).
    7. Nitu Kumari & Nishith Mohan, 2019. "Cross Diffusion Induced Turing Patterns in a Tritrophic Food Chain Model with Crowley-Martin Functional Response," Mathematics, MDPI, vol. 7(3), pages 1-25, March.
    8. 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).
    9. 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.
    10. Zhang, Shengqiang & Yuan, Sanling & Zhang, Tonghua, 2022. "A predator-prey model with different response functions to juvenile and adult prey in deterministic and stochastic environments," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    11. 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).
    12. 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.
    13. Souna, Fethi & Lakmeche, Abdelkader & Djilali, Salih, 2020. "Spatiotemporal patterns in a diffusive predator-prey model with protection zone and predator harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    14. 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.
    15. 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).
    16. 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.
    17. 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).
    18. 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).
    19. Meng, Xin-You & Huo, Hai-Feng & Xiang, Hong & Yin, Qi-yu, 2014. "Stability in a predator–prey model with Crowley–Martin function and stage structure for prey," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 810-819.
    20. Abdul Khaliq & Tarek F. Ibrahim & Abeer M. Alotaibi & Muhammad Shoaib & Mohammed Abd El-Moneam, 2022. "Dynamical Analysis of Discrete-Time Two-Predators One-Prey Lotka–Volterra Model," Mathematics, MDPI, vol. 10(21), pages 1-30, October.

    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:jnlaaa:v:2014:y:2014:i:1:n:169609. 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/4058 .

    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.