Global dynamics of a diffusive phytoplankton-zooplankton model with toxic substances effect and delay

Hong Yang; Hong Yang

doi:10.3934/mbe.2022316

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 7: 6712-6730. doi: 10.3934/mbe.2022316

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Global dynamics of a diffusive phytoplankton-zooplankton model with toxic substances effect and delay

Hong Yang ^{1,2
,
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1.
School of Science, Jiangsu Ocean University, Lianyungang 222005, China
2.
Marine Resources Development Institute of Jiangsu, Jiangsu Ocean University, Liangyungang 222005, China

Academic Editor: Frithjof Lutscher

Received: 22 January 2022 Revised: 15 March 2022 Accepted: 07 April 2022 Published: 29 April 2022

This paper examines a diffusive toxic-producing plankton system with delay. We first show the global attractivity of the positive equilibrium of the system without time-delay. We further consider the effect of delay on asymptotic behavior of the positive equilibrium: when the system undergoes Hopf bifurcation at some points of delay by the normal form and center manifold theory for partial functional differential equations. Global existence of periodic solutions is established by applying the global Hopf bifurcation theory.
- reaction-diffusion,
- delay,
- phytoplankton-zooplankton model,
- Hopf bifurcation,
- global periodic solutions
Citation: Hong Yang. Global dynamics of a diffusive phytoplankton-zooplankton model with toxic substances effect and delay[J]. Mathematical Biosciences and Engineering, 2022, 19(7): 6712-6730. doi: 10.3934/mbe.2022316

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Abstract

This paper examines a diffusive toxic-producing plankton system with delay. We first show the global attractivity of the positive equilibrium of the system without time-delay. We further consider the effect of delay on asymptotic behavior of the positive equilibrium: when the system undergoes Hopf bifurcation at some points of delay by the normal form and center manifold theory for partial functional differential equations. Global existence of periodic solutions is established by applying the global Hopf bifurcation theory.

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