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Stability and dynamical analysis of a biological system. (English) Zbl 1474.92135

Summary: 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.

MSC:

92D40 Ecology
92D25 Population dynamics (general)
35K51 Initial-boundary value problems for second-order parabolic systems
35Q92 PDEs in connection with biology, chemistry and other natural sciences
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