IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v41y2009i4p1634-1644.html
   My bibliography  Save this article

Spatiotemporal complexity of a predator–prey system with the effect of noise and external forcing

Author

Listed:
  • Rao, Feng
  • Wang, Weiming
  • Li, Zhenqing

Abstract

In this paper, we present a spatial version of the Ivlev-type predator–prey model which contains some important factors, such as noise on predator, external periodic forcing and diffusion processes on both predator and prey. From the numerical results, we know that noise or external periodic forcing can induce instability and enhance the oscillation of the species density, and the cooperation between noise and external periodic forcing inherent to the deterministic dynamics of periodically driven models gives rise to the appearance of a rich transport phenomenology. Furthermore, we demonstrate that the spatially extended system exhibits a resonant patterns and frequency-locking phenomena. Our results show that noise and external periodic forcing play a prominent role in the predator–prey model.

Suggested Citation

  • Rao, Feng & Wang, Weiming & Li, Zhenqing, 2009. "Spatiotemporal complexity of a predator–prey system with the effect of noise and external forcing," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1634-1644.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:4:p:1634-1644
    DOI: 10.1016/j.chaos.2008.07.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007790800307X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2008.07.005?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. Gakkhar, Sunita & Singh, Brahampal, 2006. "Dynamics of modified Leslie–Gower-type prey–predator model with seasonally varying parameters," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1239-1255.
    2. Huang, Jicai & Jing, Zhujun, 2009. "Bifurcations and chaos in three-well Duffing system with one external forcing," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1449-1466.
    3. Gan, Chunbiao, 2006. "Noise-induced chaos in a quadratically nonlinear oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 30(4), pages 920-929.
    4. La Barbera, A & Spagnolo, B, 2002. "Spatio-temporal patterns in population dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 120-124.
    5. F. N. Si & Q. X. Liu & J. Z. Zhang & L. Q. Zhou, 2007. "Propagation of travelling waves in sub-excitable systems driven by noise and periodic forcing," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 60(4), pages 507-513, December.
    6. Burić, Nikola & Todorović, Kristina & Vasović, Nebojša, 2009. "Dynamics of noisy FitzHugh–Nagumo neurons with delayed coupling," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2405-2413.
    7. Wang, Hailing & Wang, Weiming, 2008. "The dynamical complexity of a Ivlev-type prey–predator system with impulsive effect," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1168-1176.
    8. Spagnolo, B. & La Barbera, A., 2002. "Role of the noise on the transient dynamics of an ecosystem of interacting species," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 315(1), pages 114-124.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zhang, Xue & Zhang, Qing-Ling & Liu, Chao & Xiang, Zhong-Yi, 2009. "Bifurcations of a singular prey–predator economic model with time delay and stage structure," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1485-1494.
    2. Huang, Tousheng & Zhang, Huayong, 2016. "Bifurcation, chaos and pattern formation in a space- and time-discrete predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 92-107.
    3. 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).
    4. Ghorai, Santu & Poria, Swarup, 2016. "Pattern formation and control of spatiotemporal chaos in a reaction diffusion prey–predator system supplying additional food," Chaos, Solitons & Fractals, Elsevier, vol. 85(C), pages 57-67.
    5. Mortuja, Md Golam & Chaube, Mithilesh Kumar & Kumar, Santosh, 2021. "Dynamic analysis of a predator-prey system with nonlinear prey harvesting and square root functional response," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).

    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. Bashkirtseva, Irina & Ryashko, Lev & Ryazanova, Tatyana, 2019. "Stochastic variability and transitions to chaos in a hierarchical three-species population model," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 276-283.
    2. Valenti, D. & Tranchina, L. & Brai, M. & Caruso, A. & Cosentino, C. & Spagnolo, B., 2008. "Environmental metal pollution considered as noise: Effects on the spatial distribution of benthic foraminifera in two coastal marine areas of Sicily (Southern Italy)," Ecological Modelling, Elsevier, vol. 213(3), pages 449-462.
    3. Djilali, Salih & Cattani, Carlo, 2021. "Patterns of a superdiffusive consumer-resource model with hunting cooperation functional response," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    4. Mandal, Partha Sarathi & Banerjee, Malay, 2012. "Stochastic persistence and stationary distribution in a Holling–Tanner type prey–predator model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1216-1233.
    5. Jin, Yanfei & Wang, Heqiang, 2020. "Noise-induced dynamics in a Josephson junction driven by trichotomous noises," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    6. Wang, Weiming & Wang, Xiaoqin & Lin, Yezhi, 2008. "Complicated dynamics of a predator–prey system with Watt-type functional response and impulsive control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1427-1441.
    7. Liu, Jian & Qiao, Zijian & Ding, Xiaojian & Hu, Bing & Zang, Chuanlai, 2021. "Stochastic resonance induced weak signal enhancement over controllable potential-well asymmetry," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    8. Chun Zhang & Tao Yang & Shi-Xian Qu, 2021. "Impact of time delays and environmental noise on the extinction of a population dynamics model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(11), pages 1-16, November.
    9. Zhang, Wenyue & Shi, Peiming & Li, Mengdi & Han, Dongying, 2021. "A novel stochastic resonance model based on bistable stochastic pooling network and its application," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    10. Enrico Sciubba, 2019. "The Exergy Footprint as a Sustainability Indicator: An Application to the Neanderthal–Sapiens Competition in the Late Pleistocene," Sustainability, MDPI, vol. 11(18), pages 1-20, September.
    11. Ai, Hao & Yang, GuiJiang & Liu, Wei & Wang, Qiubao, 2023. "A fast search method for optimal parameters of stochastic resonance based on stochastic bifurcation and its application in fault diagnosis of rolling bearings," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    12. Wang, Xiaoqin & Wang, Weiming & Lin, Yezhi & Lin, Xiaolin, 2009. "The dynamical complexity of an impulsive Watt-type prey–predator system," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 731-744.
    13. Dong, Yang & Wen, Shu-hui & Hu, Xiao-bing & Li, Jiang-Cheng, 2020. "Stochastic resonance of drawdown risk in energy market prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    14. Gakkhar, Sunita & Sahani, Saroj Kumar, 2009. "A model for delayed effect of toxicant on resource-biomass system," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 912-922.
    15. Ling, Li & Wang, Weiming, 2009. "Dynamics of a Ivlev-type predator–prey system with constant rate harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2139-2153.
    16. Gan, Chunbiao & He, Shimin, 2008. "Surrogate test for noise-contaminated dynamics in the Duffing oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1517-1522.
    17. Akgül, Akif & Rajagopal, Karthikeyan & Durdu, Ali & Pala, Muhammed Ali & Boyraz, Ömer Faruk & Yildiz, Mustafa Zahid, 2021. "A simple fractional-order chaotic system based on memristor and memcapacitor and its synchronization application," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    18. Liao, Tiancai, 2022. "The impact of plankton body size on phytoplankton-zooplankton dynamics in the absence and presence of stochastic environmental fluctuation," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    19. Kim, Hye Kyung & Baek, Hunki, 2013. "The dynamical complexity of a predator–prey system with Hassell–Varley functional response and impulsive effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 94(C), pages 1-14.
    20. Jiang, Zhichao & Wei, Junjie, 2008. "Stability and bifurcation analysis in a delayed SIR model," Chaos, Solitons & Fractals, Elsevier, vol. 35(3), pages 609-619.

    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:eee:chsofr:v:41:y:2009:i:4:p:1634-1644. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.