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Dynamics in a diffusive plankton system with time delay and Tissiet functional response

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Abstract

Based on the study of the plankton population system, a diffusive toxic plankton model with Tissiet type functional response function and predation delay is proposed. Firstly, the sufficient conditions for locally asymptotic stability of the diffusion system without delay at the positive equilibrium are given, the existence conditions of Hopf bifurcation caused by diffusion are given, and the conditions under which diffusion makes spatially homogeneous and nonhomogeneous periodic solutions bifurcate from the positive constant equilibrium are given. Secondly, the time delay effect on the plankton reaction–diffusion system is studied, the existence of Hopf bifurcation at the positive equilibrium induced by delay is discussed. By applying the central manifold theory and normal form method of partial functional differential equations, the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are studied. Finally, the reliability of theoretical research is verified by numerical simulation.

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Authors and Affiliations

  1. College of Mathematical Sciences, Harbin Engineering University, Harbin, 150001, Heilongjiang, People’s Republic of China

    Haicheng Liu, Bin Ge, Jiaqi Chen & Qiyuan Liang

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  1. Haicheng Liu
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  2. Bin Ge
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  4. Qiyuan Liang
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Correspondence to Bin Ge.

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Liu, H., Ge, B., Chen, J. et al. Dynamics in a diffusive plankton system with time delay and Tissiet functional response. J. Appl. Math. Comput. 68, 1313–1334 (2022). https://doi.org/10.1007/s12190-021-01568-z

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  • DOI: https://doi.org/10.1007/s12190-021-01568-z

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