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Volume 10, Number 2, 2020, Pages 686-712                                                                DOI:10.11948/20190094
Spatiotemporal complexity of a diffusive planktonic system with prey-taxis and toxic effects
Kejun Zhuang,Wenqian You,Gao Jia
Keywords:Planktonic system, reaction diffusion, prey-taxis, linear stability, steady state bifurcation, Hopf bifurcation.
      In this paper, we propose a three-species reaction-diffusion planktonic system with prey-taxis and toxic effects, in which the zooplankton can recognize the nontoxic and toxin-producing phytoplankton and can make proper response. We first establish the existence and stability of the unique positive constant equilibrium solution by utilizing the linear stability theory for partial differential equations. Then we obtain the existence and properties of nonconstant positive solutions by detailed steady state bifurcation analysis. In addition, we obtain that change of taxis rate will result in the appearance of time-periodic solutions. Finally, we conduct some numerical simulations and give the conclusions.
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