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Dynamic behavior analysis of a diffusive plankton model with defensive and offensive effects

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  • Zhao, Qiuyue
  • Liu, Shutang
  • Niu, Xinglong

Abstract

This paper investigates the dynamic behavior of a diffusive plankton model with defensive and offensive effects in two cases. For the single compartment model, we first derive the sufficient conditions for the stability and Hopf bifurcation of coexisting equilibrium, which implies that the changes of defense and offense can cause oscillation of planktonic population. Then the properties of Hopf bifurcation are discussed by center manifold theorem. For the spatially extended model, we obtain the sufficient conditions for Turing instability and Hopf bifurcation. It is observed that spatial patterns put in place, under the interaction of diffusion, defense and offense. Finally, some numerical simulations are carried out to support the analytical results.

Suggested Citation

  • Zhao, Qiuyue & Liu, Shutang & Niu, Xinglong, 2019. "Dynamic behavior analysis of a diffusive plankton model with defensive and offensive effects," Chaos, Solitons & Fractals, Elsevier, vol. 129(C), pages 94-102.
    • Handle: RePEc:eee:chsofr:v:129:y:2019:i:c:p:94-102
    DOI: 10.1016/j.chaos.2019.08.015
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    References listed on IDEAS

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    1. Zhao, Qiuyue & Liu, Shutang & Tian, Dadong, 2018. "Dynamic behavior analysis of phytoplankton–zooplankton system with cell size and time delay," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 160-168.
    2. Wu, Ranchao & Zhou, Yue & Shao, Yan & Chen, Liping, 2017. "Bifurcation and Turing patterns of reaction–diffusion activator–inhibitor model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 597-610.
    3. Shi, Renxiang & Yu, Jiang, 2017. "Hopf bifurcation analysis of two zooplankton-phytoplankton model with two delays," Chaos, Solitons & Fractals, Elsevier, vol. 100(C), pages 62-73.
    4. Mougi, Akihiko, 2012. "Predator–prey coevolution driven by size selective predation can cause anti-synchronized and cryptic population dynamics," Theoretical Population Biology, Elsevier, vol. 81(2), pages 113-118.
    5. Huang, Dongwei & Wang, Hongli & Feng, Jianfeng & Zhu, Zhi-wen, 2006. "Hopf bifurcation of the stochastic model on HAB nonlinear stochastic dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 1072-1079.
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