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Dynamical Complexity of a Spatial Phytoplankton‐Zooplankton Model with an Alternative Prey and Refuge Effect

Author

Listed:
  • Weiwei Zhang
  • Min Zhao

Abstract

The spatiotemporal dynamics of a phytoplankton‐zooplankton model with an alternative prey and refuge effect is investigated mathematically and numerically. The stability of the equilibrium point and the traveling wave solution of the phytoplankton‐zooplankton model are described based on theoretical mathematical work, which provides the basis of the numerical simulation. The numerical analysis shows that refuges have a strong effect on the spatiotemporal dynamics of the model according to the pattern formation. These results may help us to understand prey‐predator interactions in water ecosystems. They are also relevant to research into phytoplankton‐zooplankton ecosystems.

Suggested Citation

  • Weiwei Zhang & Min Zhao, 2013. "Dynamical Complexity of a Spatial Phytoplankton‐Zooplankton Model with an Alternative Prey and Refuge Effect," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:608073
    DOI: 10.1155/2013/608073
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    References listed on IDEAS

    as
    1. 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).
    2. Das, Kalyan & Gazi, Nurul Huda, 2011. "Random excitations in modelling of algal blooms in estuarine systems," Ecological Modelling, Elsevier, vol. 222(14), pages 2495-2501.
    3. 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, Hindawi, vol. 2012, pages 1-17, April.
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    Cited by:

    1. Pengfei Wang & Min Zhao & Hengguo Yu & Chuanjun Dai & Nan Wang & Beibei Wang, 2016. "Nonlinear Dynamics of a Toxin‐Phytoplankton‐Zooplankton System with Self‐ and Cross‐Diffusion," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).
    2. Xinhong Pan & Min Zhao & Chuanjun Dai & Yapei Wang, 2014. "Stability and Hopf Bifurcation Analysis of a Nutrient‐Phytoplankton Model with Delay Effect," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    3. Nan Wang & Min Zhao & Hengguo Yu & Chuanjun Dai & Beibei Wang & Pengfei Wang, 2016. "Bifurcation Behavior Analysis in a Predator‐Prey Model," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).

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