Dynamics of a diffusive autotrophs–mixotrophs interaction model in a poorly mixed water column

Mixotrophs can prey on micro-autotrophic algae and also can compete with autotrophs for light and nutrients, forming an intraguild predation structure. In order to capture this character of mixotrophs and describe the autotrophs–mixotrophs interactions in a poorly mixed water column, we develop a reaction–diffusion model. The dynamics of this system, including dissipation, Turing instability, existence and stability of constant steady state solutions, and existence and nonexistence of nonconstant steady state solutions, are well explored. The influence of the autotrophic behavior of mixotrophs on autotrophs and mixotrophs biomass density is also considered by using extensive simulations. The result of numerical simulation shows that the proportion of autotrophic behaviors of mixotrophs plays an important role, affecting the coexistence of autotrophs and mixotrophs, beneficial to phytoplankton biodiversity.