Asymptotic Behavior of a Stochastic Generalized Nutrient–Phytoplankton–Zooplankton Model

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Nonlinear Science Pub Date : 2024-08-16 DOI:10.1007/s00332-024-10070-2

Peng Li, Xiaofeng Zhang, Rong Yuan

引用次数: 0

Abstract

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.

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随机广义营养物-浮游植物-浮游动物模型的渐近行为

本文考虑了具有营养循环的随机营养-浮游植物-浮游动物模型。为了将随机波动考虑在内，我们在营养、浮游植物和浮游动物生物量变化的时间间隔（\△t\）内加入随机增量，从而得到相应的随机模型。随后，我们探讨了全局正解的存在性、唯一性和随机终极约束性。通过构造合适的 Lyapunov 函数，我们还得到了该模型的 V 几何遍历性。此外，我们还建立了指数消亡和浮游生物均值持久性的充分条件。最后，我们给出了一些数值模拟来验证理论结果，并分析了一些重要参数的影响。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Nonlinear Science 数学-力学

CiteScore

5.00

自引率

3.30%

发文量

审稿时长

4.5 months

期刊介绍： The mission of the Journal of Nonlinear Science is to publish papers that augment the fundamental ways we describe, model, and predict nonlinear phenomena. Papers should make an original contribution to at least one technical area and should in addition illuminate issues beyond that area''s boundaries. Even excellent papers in a narrow field of interest are not appropriate for the journal. Papers can be oriented toward theory, experimentation, algorithms, numerical simulations, or applications as long as the work is creative and sound. Excessively theoretical work in which the application to natural phenomena is not apparent (at least through similar techniques) or in which the development of fundamental methodologies is not present is probably not appropriate. In turn, papers oriented toward experimentation, numerical simulations, or applications must not simply report results without an indication of what a theoretical explanation might be. All papers should be submitted in English and must meet common standards of usage and grammar. In addition, because ours is a multidisciplinary subject, at minimum the introduction to the paper should be readable to a broad range of scientists and not only to specialists in the subject area. The scientific importance of the paper and its conclusions should be made clear in the introduction-this means that not only should the problem you study be presented, but its historical background, its relevance to science and technology, the specific phenomena it can be used to describe or investigate, and the outstanding open issues related to it should be explained. Failure to achieve this could disqualify the paper.