Plankton growth dynamic driven by plankton body size in deterministic
and stochastic environments
Abstract
In this paper, we establish a new phytoplankton-zooplankton model by
considering the effects of plankton body size and stochastic
environmental fluctuations. Mathematical theory work mainly gives the
existence of boundary and positive equilibria, and shows their local as
well as global stability in the deterministic model. Additionally, we
explore the dynamics of V-geometric ergodicity, stochastic ultimate
boundedness, stochastic permanence, persistence in the mean, stochastic
extinction and the existence of a unique ergodic stationary distribution
in the corresponding stochastic version. Numerical simulation work
mainly reveals that plankton body size can generate great influences on
the interactions between phytoplankton and zooplankton, which in turn
proves the effectiveness of mathematical theory analysis. It is worth
emphasizing that for the small value of phytoplankton cell size, the
increase of zooplankton body size can not change the phytoplankton
density or zooplankton density; for the middle value of phytoplankton
cell size, the increase of zooplankton body size can decrease
zooplankton density or phytoplankton density; for the large value of
phytoplankton body size, the increase of zooplankton body size can
increase zooplankton density but decrease phytoplankton density.
Besides, it should be noted that the increase of zooplankton body size
can not affect the effect of random environmental disturbance, while the
increase of phytoplankton cell size can weaken its effect. There results
may enrich the dynamics of phytoplankton-zooplankton models.