The Effect of Weakly Nonlinear Diffusion

Plankton communities play a significant role in the global biosphere, especially in the marine ecosystem. They, floated in the surface water, are composed of phytoplankton (prey) and zooplankton (predators) in which the zooplankton aggregates to be small groups, cooperatively forages phytoplankton, and grows nonlinearly and adaptively to form predation strategies and to avoid fierce interspecific competition. It is well known that plankton communities constitute the beginning role in food chains and support the property of marine lives [318]. Importantly, phytoplankton and zooplankton are two kinds of the most important planktons in the plankton communities. For instance, phytoplankton drifts on the surface water to obtain sunlight for photosynthesis, while zooplankton has ability to swim and feeds on phytoplankton [297]. Hence, phytoplankton (prey) and zooplankton (predators) compose a microalgae ecosystem by their interaction effects on the survival of both. Especially, phytoplankton in plankton communities can grow increasingly or decreasingly, giving rise to be a slow-fast processes rapidly [307, 311]. Sometimes, researchers call the high concentration of phytoplankton in the surface water by growth rapidly as “bloom” from the perspective of anthropocentrism [263]. To solve the “bloom” harm, fortunately, researchers found out that zooplankton can prey on phytoplankton [264] and contribute to preventing the rapid growth of phytoplankton [249].