Dynamical analysis on stochastic two-species models

IF 1.1 4区数学 Q2 MATHEMATICS, APPLIED

Applicable Analysis Pub Date : 2023-10-16 DOI:10.1080/00036811.2023.2270214

Guangbin Wang, Jingliang Lv, Xiaoling Zou

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引用次数: 0

Abstract

AbstractIn this paper, we study three stochastic two-species models. We construct the stochastic models corresponding to its deterministic model by introducing stochastic noise into the equations. For the first model, we show that the system has a unique global solution starting from the positive initial value. In addition, we discuss the extinction and the existence of stationary distribution under some conditions. For the second system, we explore the existence and uniqueness of the solution. Then we obtain sufficient conditions for global asymptotic stability of the equilibrium point and the positive recurrence of solution. For the last model, the existence and uniqueness of solution, the sufficient conditions for extinction and asymptotic stability and the positive recurrence of solution and weak persistence are derived. And numerical simulations are performed to support our results.Keywords: Stabilityextinctionstationary distributionpositive recurrenceweak persistenceMathematics Subject Classifications: 60G1560G4460G5260H10 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis research was supported by Natural Science Foundation of Shandong Province, China [grant number ZR2020MA038] and [grant number ZR2020MA037].

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随机两种模型的动力学分析

摘要本文研究了三种随机两种模型。通过在方程中引入随机噪声，构造了与其确定性模型相对应的随机模型。对于第一个模型，我们证明了系统从正初值开始具有唯一的全局解。此外，我们还讨论了在某些条件下平稳分布的消光性和存在性。对于第二个系统，我们探讨了解的存在唯一性。得到了平衡点全局渐近稳定的充分条件和解的正递推性。对于最后一个模型，给出了解的存在唯一性、消光和渐近稳定的充分条件、解的正递推性和弱持久性。并进行了数值模拟。关键词:稳定性消去平稳分布正递归弱持续性数学学科分类:60G1560G4460G5260H10披露声明作者未报告潜在利益冲突。本研究得到山东省自然科学基金[批准号ZR2020MA038]和[批准号ZR2020MA037]的支持。

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来源期刊

Applicable Analysis 数学-应用数学

CiteScore

2.60

自引率

9.10%

发文量

175

审稿时长

2 months

期刊介绍： Applicable Analysis is concerned primarily with analysis that has application to scientific and engineering problems. Papers should indicate clearly an application of the mathematics involved. On the other hand, papers that are primarily concerned with modeling rather than analysis are outside the scope of the journal General areas of analysis that are welcomed contain the areas of differential equations, with emphasis on PDEs, and integral equations, nonlinear analysis, applied functional analysis, theoretical numerical analysis and approximation theory. Areas of application, for instance, include the use of homogenization theory for electromagnetic phenomena, acoustic vibrations and other problems with multiple space and time scales, inverse problems for medical imaging and geophysics, variational methods for moving boundary problems, convex analysis for theoretical mechanics and analytical methods for spatial bio-mathematical models.