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Dynamical analysis of a reaction-diffusion phytoplankton-zooplankton system with delay

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  • Jiang, Zhichao
  • Zhang, Tongqian

Abstract

A phytoplankton-zooplankton system with the delay and reaction-diffusion term is investigated. Firstly, existence and priori bound of solution without delay system are given. The stability of the axial steady state solution with delay system are analyzed by using the comparison arguments and modifying the coupled lower-upper solution pairs. By considering the effects of delay and diffusion, the stability and Hopf bifurcation of the positive steady state solution is investigated. When the delay does not exist, the diffusion cannot vary the stability of the steady state solutions, that is, the Turing instability cannot occur. When the delay exists, the effects of big and small diffusions to Hopf bifurcation are investigated, under certain conditions, the space inhomogeneous periodic solutions may produce. Furthermore, the algorithm determining the properties of bifurcation periodic solutions is given. At last, some numerical simulations are carried out to confirm the correctness of theoretical analyses.

Suggested Citation

  • Jiang, Zhichao & Zhang, Tongqian, 2017. "Dynamical analysis of a reaction-diffusion phytoplankton-zooplankton system with delay," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 693-704.
    • Handle: RePEc:eee:chsofr:v:104:y:2017:i:c:p:693-704
    DOI: 10.1016/j.chaos.2017.09.030
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    References listed on IDEAS

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    1. Zhao, Jiantao & Wei, Junjie, 2009. "Stability and bifurcation in a two harmful phytoplankton–zooplankton system," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1395-1409.
    2. Roy, Shovonlal, 2009. "The coevolution of two phytoplankton species on a single resource: Allelopathy as a pseudo-mixotrophy," Theoretical Population Biology, Elsevier, vol. 75(1), pages 68-75.
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    Cited by:

    1. 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).
    2. Liang, Yuqin & Jia, Yunfeng, 2022. "Stability and Hopf bifurcation of a diffusive plankton model with time-delay and mixed nonlinear functional responses," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).

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