Abstract
We studied a plankton community composed of phytoplankton (prey) and zooplankton (predators). The zooplankton forms small groups, cooperatively forages phytoplankton, and disperses nonlinearly to adapt to predation strategies and to avoid fierce interspecific competition. First, through linear stability analysis, we obtained the conditions of Hopf stability and the Turing bifurcation. Second, weakly nonlinear analysis helped us establish the amplitude equations that determine the type of patterns: spot patterns, stripe patterns, and mixed patterns of both kinds. Finally, the numerical simulations illustrate the stability of the system and the self-organizing behaviors of planktons. The results partly validate our analysis and help us better understand the dynamics of the algae ecosystem in the real world. Furthermore, we found that the weakly nonlinear analysis, as a tool, can be applied to the model without linearizing the weakly nonlinear diffusion, which extends the application scope of the tool.
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