Dynamics of a stochastic phytoplankton-toxin phytoplankton–zooplankton model

Abstract

Environmental fluctuations and toxin-producing phytoplankton are crucial factors affecting marine ecosystems. In this paper, we propose a stochastic phytoplankton-toxin phytoplankton-zooplankton model to study the effect of environmental fluctuations on extinction and persistence of the population. The results show that large environmental fluctuations may lead to the extinction of the population, and small environmental fluctuation can keep population weakly persistent in the mean. We also find that the noise-induced extinction of one phytoplankton population may lead to the density increase of the other phytoplankton population in two competitive phytoplankton populations. By constructing appropriate Lyapunov functions, we obtain the sufficient conditions for the existence of an ergodic stationary distribution of the model. Finally, numerical simulations are carried out to support our main results.

Stationary distribution and extinction of a stochastic nutrient‐phytoplankton‐zooplankton model with cell size

“…20 Stochastic stability and existence of stochastic Hopf bifurcation are also discussed based on singular boundary theory of diffusion process and invariant measure theory. 21 Chen et al 22 finds that the noise-induced extinction of one phytoplankton population may lead to the density increase of the other phytoplankton population in two competitive phytoplankton populations.…”

Analysis on dynamical behavior of a stochastic phytoplankton‐zooplankton model with nonlinear perturbation

“…In recent years, the study of plankton model is a hot topic in water ecosystem. [1][2][3][4][5][6][7][8][9][10][11][12][13] Phytoplankton is the primary producer of aquatic ecology, which consumes half of the carbon dioxide and releases half of the oxygen through photosynthesis all over the world. Phytoplankton and zooplankton, as the middle and bottom layers of the food chain of aquatic ecosystems, play a pivotal role in maintaining the global climate.…”

“…Environmental noise can just reflect the influence of external factors on the deterministic model. [6][7][8][9][10][11][12][13] For example, Majumder et al 7 compared the dynamic results of the deterministic phytoplankton-zooplankton model with its corresponding stochastic model. Yu et al 12 proved the existence condition of extinction and persistence of the population on a stochastic phytoplankton-toxin phytoplankton-zooplankton.…”

“…In recent years, the study of plankton model is a hot topic in water ecosystem 1–13 . Phytoplankton is the primary producer of aquatic ecology, which consumes half of the carbon dioxide and releases half of the oxygen through photosynthesis all over the world.…”

“…There are, however, some limitations of the present study, as it does not reflect the impact of the environmental external factors including climate change, humidity, temperature, and so on. Environmental noise can just reflect the influence of external factors on the deterministic model 6–13 . For example, Majumder et al 7 compared the dynamic results of the deterministic phytoplankton‐zooplankton model with its corresponding stochastic model.…”