Asymptotic behavior of a stochastic generalized nutrient-phytoplankton-zooplankton model. (English) Zbl 07923953
Summary: In this paper, we consider the stochastic nutrient-phytoplankton-zooplankton model with nutrient cycle. In order to take stochastic fluctuations into account, we add the stochastic increments to the variations of biomass of nutrition, phytoplankton and zooplankton during time interval \(\Delta t\), thus we obtain the corresponding stochastic model. Subsequently, we explore the existence, uniqueness and stochastically ultimate boundness of global positive solution. By constructing suitable Lyapunov function, we also obtain \(V\)-geometric ergodicity of this model. In addition, the sufficient conditions of exponential extinction and persistence in the mean of plankton are established. At last, we present some numerical simulations to validate theoretical results and analyze the impacts of some important parameters.
MSC:
| 37A50 | Dynamical systems and their relations with probability theory and stochastic processes |
| 37H30 | Stability theory for random and stochastic dynamical systems |
| 39A50 | Stochastic difference equations |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 92-10 | Mathematical modeling or simulation for problems pertaining to biology |
Keywords:
stochastic nutrient-phytoplankton-zooplankton model; \(V\)-geometric ergodicity; exponential extinction; persistence in the mean; nutrient cycleReferences:
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