A stochastic nutrient-phytoplankton model with viral infection and Markov switching

Dynamics of a stochastic phytoplankton–toxic phytoplankton–zooplankton system under regime switching

“…Actually, the work of May 36 pointed out that these small environmental fluctuations can affect the ecological parameters of a model positively or negatively, which can be described by white noise. Thus, following the idea of previous works, 26,27,30,31 the convenient formulations, which describe the intrinsic growth rates of phytoplankton populations and the death rate of zooplankton population that are influenced by white noise, are taken as r i → r i + 𝜎 i dB i (t)(i = 1, 2) and −d → −d + 𝜎 3 dB 3 (t), respectively. Here the terms dB i (t) denote the white noises and 𝜎 2 i > 0 are their intensities of white noises, i = 1, 2, 3.…”

“…Actually, the work of May 36 pointed out that these small environmental fluctuations can affect the ecological parameters of a model positively or negatively, which can be described by white noise. Thus, following the idea of previous works, 26,27,30,31 the convenient formulations, which describe the intrinsic growth rates of phytoplankton populations and the death rate of zooplankton population that are influenced by white noise, are taken as $$$ {r}_i\to {r}_i+{\sigma}_id{B}_i(t)\left(i=1,2\right) $$$ and $$$ -d\to -d+{\sigma}_3d{B}_3(t) $$$, respectively. Here the terms $$$ d{B}_i(t) $$$ denote the white noises and $$$ {\sigma}_i^2>0 $$$ are their intensities of white noises, $$$ i=1,2,3 $$$. We further consider the regime switching into the model, where the biomass of plankton often suffer switching abruptly to a contrasting alternative stable state in the real world due to some kinds of moderate environmental fluctuations, for example, environmental pollution, rain falls, 37,38 and biotic exploitation 39 .…”

“…In addition, the growth rate of toxic Microcystis and environmental biomass rely heavily on the temperature and nutrient concentration 24,25 . Thus, plankton systems with environmental fluctuations are significantly more reasonable, and the issue of how environmental fluctuations affect plankton systems has attracted increasing attention and great effort has been made towards the study of the dynamics of stochastic plankton systems recently 26–32 . But the study of stochastic phytoplankton–toxic phytoplankton–zooplankton system is still in its infancy, especially the dynamics of the phytoplankton–toxin‐producing phytoplankton–zooplankton system with white noise and regime switching is currently unclear.…”

“…24,25 Thus, plankton systems with environmental fluctuations are significantly more reasonable, and the issue of how environmental fluctuations affect plankton systems has attracted increasing attention and great effort has been made towards the study of the dynamics of stochastic plankton systems recently. [26][27][28][29][30][31][32] But the study of stochastic phytoplankton-toxic phytoplankton-zooplankton system is still in its infancy, especially the dynamics of the phytoplankton-toxin-producing phytoplankton-zooplankton system with white noise and regime switching is currently unclear. Thus, we mainly present the effects of white noise, regime switching, and toxic substances produced by TPP on the stochastic phytoplankton-toxic phytoplankton-zooplankton system in this paper.…”

Stationary Probability Density Analysis for the Randomly Forced Phytoplankton–Zooplankton Model with Correlated Colored Noises

“…Species concentrations, however, are susceptible to fluctuations in the real environment that can not be neglected when seeking a better understanding of the dynamics of complex living systems [24][25][26][27][28][29][30][31][32]. This is especially true for marine organisms due to the unpredictability of water temperature, nutrient availability, photosynthetically active radiation and other physical factors embedded in aquatic ecosystems [33][34][35][36]. Consequently, nonlinear stochastic ecosystem with noise term has recently attracted the attention of scholars [37][38][39][40][41].…”