具有双随机扰动驱动的一般函数响应的随机捕食-食饵模型的渐近性质

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-02-21 DOI:10.1002/mma.10825

Fethi Souna

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引用次数: 0

摘要

本文研究了一个由两个微分方程组成的广义随机捕食者-猎物模型，该模型具有一般非线性泛函响应，表示为F (u, v) $$ F\left(u,v\right) $$，由标准布朗运动和l杂讯驱动。与先前的研究不同，本文的主要目的是研究系统的长期行为，同时只对功能反应进行温和的假设。我们的分析建立了一个全局正解的存在唯一性。此外，我们还利用新的阈值参数推导了两种物种灭绝和持续存在的充分条件。值得注意的是，这些结果的推导和证实使用了一个l杂讯型扰动，而不要求l杂讯有界；也就是说，我们不假设（𝕐）＆lt；∞。

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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Asymptotic Properties of a Stochastic Predator–Prey Model With a General Functional Response Driven by Dual Stochastic Perturbations

This paper investigates a generalized stochastic predator-prey model consisting of two differential equations with a general nonlinear functional response denoted as $F (u, v)$ , driven by both standard Brownian motion and Lévy noise. Unlike prior research, the main objective of this manuscript is to investigate the long-term behavior of the system while placing only mild assumptions on the functional response. Our analysis establishes the existence and uniqueness of a global positive solution. Moreover, we derive sufficient conditions for the extinction and persistence of the two species by employing novel threshold parameters. Notably, these outcomes are derived and substantiated using a Lévy-type perturbation by not requiring that the Lévy noise be bounded; that is, we do not assume $ϑ (𝕐) < \infty$ .

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.