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

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  • 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
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    References listed on IDEAS

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    1. Gan, Chunbiao, 2006. "Noise-induced chaos in a quadratically nonlinear oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 30(4), pages 920-929.
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    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.
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    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).

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