包含加性阿利效应的分数阶逻辑方程的建模与分析

Preety Kalra, Nisha Malhotra
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引用次数: 0

摘要

本研究利用卡普托分数阶微分方程研究了包含加性阿利效应的单一物种逻辑模型。阿利效应描述了低密度时个体适应性与种群密度之间的正相关关系。当种群数量低于临界水平时,受强阿利效应影响的种群会走向灭绝。本研究计算了受强阿利效应影响的种群的临界水平。各种已发表的研究表明,分数阶模型比普通整数阶系统更适合解释现实世界的现象;因此,本研究使用了卡普托分数阶导数。单物种模型已广泛应用于数学生物学领域,如昆虫控制、最佳生物资源规划、流行病的避免和控制以及细胞生长调节等。这项研究可以利用人工策略,使脆弱物种受到强烈的阿利效应影响,从而帮助拯救濒临灭绝的脆弱物种,并消灭不受欢迎的物种。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Modeling and Analysis of Fractional Order Logistic Equation Incorporating Additive Allee Effect
This study investigates the logistic model of a single species incorporating the additive Allee effect using Caputo fractional order differential equations. The Allee effect describes a positive correlation between individual fitness and population density at low densities. Populations subjected to the strong Allee effect can move towards extinction when their population is below a critical level. This study calculates the threshold level of the population suffering from the strong Allee effect. Various published studies are showing that fractional order models are more appropriate for explaining real-world phenomena than ordinary integer-order systems; therefore, this study involves the use of the Caputo fractional order derivative. Single-species models have been extensively used in mathematical biology, such as insect control, optimal biological resource planning, epidemic avoidance and control, and cell growth regulation. This study can help save vulnerable species from extinction and eliminate unwanted species by subjecting them to a strong Allee effect using artificial strategies.
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