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Stability and Hopf bifurcation of a diffusive plankton model with time-delay and mixed nonlinear functional responses

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  • Liang, Yuqin
  • Jia, Yunfeng

Abstract

In this paper, we deal with a plankton reaction–diffusion model with time-delay and two different functional responses. Firstly, we consider the global stability of boundary equilibrium point. Secondly, we investigate the existence, uniqueness and stability of internal equilibrium point without time-delay. Then, we analyze the existence of Hopf bifurcation emitting from internal equilibrium point and give some characteristics on Hopf branch in detail. A new finding is presented, specifically, we find that there exist two critical values which have important effects on the occurrence of Hopf bifurcation. Finally, a few numerical examples are presented to check and illustrate the theoretical analysis, some simulation graphs, including the spatiotemporal graphs, trajectory graphs and phase portraits are depicted graphically.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:163:y:2022:i:c:s0960077922007305
    DOI: 10.1016/j.chaos.2022.112533
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    References listed on IDEAS

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