Abstract
This study considers the spatiotemporal dynamics of a reaction-diffusion phytoplankton-zooplankton system with a double Allee effect on prey under a homogeneous boundary condition. The qualitative properties are analyzed, including the local stability of all equilibria and the global asymptotic property of the unique positive equilibrium. We also discuss the Hopf bifurcation and the steady state bifurcation of the system. These results are expected to help understand the complexity of the Allee effect and the interaction between phytoplankton and zooplankton.
Highlights
The upper layer of the ocean contains large volumes of drifting plankton, which can be divided into phytoplankton and zooplankton
We rigorously considered a Gause-type predatorprey model with a double Allee effect on prey, which was formulated as (4)
It is known that the predator-prey model with the most usual form of Allee effect has a unique limit cycle, but the existence of two limit cycles was proved by Gonzalez-Olivares et al [29] with a double Allee effect
Summary
The upper layer of the ocean contains large volumes of drifting plankton, which can be divided into phytoplankton and zooplankton. When m > 0, (2) describes a strong Allee effect [8, 30, 31] In this case, the population growth rate decreases if the population size is below the threshold m and the population goes to extinction [29]. The plankton populations tend to move in horizontal and vertical directions due to the strong water current This movement is usually modeled by a reaction-diffusion equation. We consider the following reaction-diffusion model with constant diffusion coefficient as well as a strong Allee effect in different spatial locations within a fixed smooth bounded domain Ω ∈ Rn. We assume that the response function of the zooplankton follows the law of mass action [15]:.
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