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Cross diffusion induced spatiotemporal pattern in diffusive nutrient–plankton model with nutrient recycling

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  • Kumari, Sarita
  • Tiwari, Satish Kumar
  • Upadhyay, Ranjit Kumar

Abstract

This paper presents a mathematical model of spatiotemporal interaction between the nutrient and phytoplankton. The interaction among the constituents in nutrient–phytoplankton system has been considered with Holling type-III functional response and nutrient recycling. We have also considered the effect of cross and self-diffusion in the system. The stability analysis of non-spatial and spatial systems have been studied. We have used simulation techniques to generate patterns for cross and self-diffusive systems. We have performed the numerical simulations and observed the effect of time evolution, cross-diffusion and rate of toxin release by phytoplankton on the density distribution of species. This phenomenon is elaborately discussed in this manuscript by introducing weakly nonlinear analysis. We also introduce amplitude equations which describe the structural interpretation and the stability of Turing pattern for nutrient–phytoplankton system. Amplitude equation is derived by using multiple-scale analysis. Cross-diffusion plays an important role in Turing instability and the formation of spot, stripe and spot–stripe like patterns. It suggests the positive environmental outcomes from nutrient recycling and spatial distribution of phytoplankton in the real world situation.

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  • Kumari, Sarita & Tiwari, Satish Kumar & Upadhyay, Ranjit Kumar, 2022. "Cross diffusion induced spatiotemporal pattern in diffusive nutrient–plankton model with nutrient recycling," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 246-272.
    • Handle: RePEc:eee:matcom:v:202:y:2022:i:c:p:246-272
    DOI: 10.1016/j.matcom.2022.05.027
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    References listed on IDEAS

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    1. Abid, Walid & Yafia, Radouane & Aziz-Alaoui, M.A. & Bouhafa, Habib & Abichou, Azgal, 2015. "Diffusion driven instability and Hopf bifurcation in spatial predator-prey model on a circular domain," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 292-313.
    2. Kejun Zhuang & Ying Li & Bin Gong & Zhichao Jiang, 2021. "Stability Switches and Hopf Bifurcation Induced by Nutrient Recycling Delay in a Reaction-Diffusion Nutrient-Phytoplankton Model," Complexity, Hindawi, vol. 2021, pages 1-12, October.
    3. Yi Wang & Min Zhao & Chuanjun Dai & Yunli Deng, 2015. "The Dynamics of a Diffusive Nutrient-Algae Model Based upon the Sanyang Wetland," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-12, October.
    4. Ghorai, Santu & Poria, Swarup, 2016. "Turing patterns induced by cross-diffusion in a predator-prey system in presence of habitat complexity," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 421-429.
    5. Debing Mei & Min Zhao & Hengguo Yu & Chuanjun Dai, 2015. "Spatiotemporal Complexity of the Nutrient-Phytoplankton Model," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-11, April.
    6. Ghorai, Santu & Chakraborty, Bhaskar & Bairagi, Nandadulal, 2021. "Preferential selection of zooplankton and emergence of spatiotemporal patterns in plankton population," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    7. Yapei Wang & Min Zhao & Chuanjun Dai & Xinhong Pan, 2014. "Nonlinear Dynamics of a Nutrient-Plankton Model," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-10, January.
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    1. Sajan, & Anshu, & Dubey, Balram, 2024. "Study of a cannibalistic prey–predator model with Allee effect in prey under the presence of diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).

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