Conditions for persistence and ergodicity of a stochastic Lotka–Volterra predator–prey model with regime switching

In this paper, we study a stochastic nutrient‐phytoplankton‐zooplankton model with cell size that represents the interaction between internal mechanism of species and external environment. We first investigate the existence and uniqueness of the global positive solution with positive initial values. Then we construct sufficient conditions for the existence of an ergodic stationary distribution of positive solution. Once more, we find that large noise intensities cause the extinctions of phytoplankton and zooplankton. Finally, numerical simulations are given to verify the correctness of theoretical results.

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“…Definition (Stochastic extinction) A population, X ( t ), is said to be stochastic extinct if

P \{\lim_{t \to + \infty} X (t) = 0\} = 1 .

…”

Section: Preliminaries and Model Descriptionmentioning

confidence: 99%

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

2020

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“…This method has been utilized by many authors (see e.g. [18,20,21]). Studying such problem is meaningful and challenging.…”

Section: Introductionmentioning

confidence: 98%

Periodic solution and stationary distribution of stochastic SIR epidemic models with higher order perturbation

Jiang

Hayat

et al. 2017

Physica A: Statistical Mechanics and its Applications

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“…In this context, many authors have introduced stochastic population models to investigate the effect of environmental variability and perturbation [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]. Here, we explore uncertainties present in the logistic model, which is commonly applied in the studies of human, plants and bacterial populations, as well as to evaluate economic growth.…”

Section: Introductionmentioning

confidence: 98%

On the logistic equation subject to uncertainties in the environmental carrying capacity and initial population density

Dorini

Cecconello

Dorini

2016

Communications in Nonlinear Science and Numerical Simulation

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Conditions for persistence and ergodicity of a stochastic Lotka–Volterra predator–prey model with regime switching

Cited by 72 publications

References 36 publications

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

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

Periodic solution and stationary distribution of stochastic SIR epidemic models with higher order perturbation

On the logistic equation subject to uncertainties in the environmental carrying capacity and initial population density

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