具有合作和狭缝效应的捕食者与猎物之间的动态相互作用:确定性和随机方法

IF 1.3 4区数学 Q3 BIOLOGY

Journal of Biological Systems Pub Date : 2022-10-26 DOI:10.1142/s0218339022500292

Biswajit Paul, Bapin Mondal, J. Ghosh, U. Ghosh

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引用次数: 3

摘要

在本文中，我们研究了具有合作和Allee效应的捕食者-猎物模型的行为，同时考虑了确定性和随机性方法。本文的主要目的是研究确定性捕食者-猎物模型中环境波动的影响。在对确定性模型的分析中，发现系统具有同维1的鞍节点、同维2的Hopf分岔和Bogdanov–Takens分岔。为了研究环境波动的影响，我们使用高斯白噪声对猎物出生率和捕食者密度死亡率的扰动。通过形成合适的李雅普诺夫函数，表明了模型和平稳分布的持久性。最后，通过数值模拟验证了理论结果。

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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DYNAMIC INTERACTIONS BETWEEN PREY AND PREDATOR WITH COOPERATION AND ALLEE EFFECT: DETERMINISTIC AND STOCHASTIC APPROACH

In this paper, we investigate the behavior of a predator–prey model with cooperation and Allee effect considering both deterministic and stochastic approaches. The main aim of this paper is to investigate the effect of environmental fluctuation in a deterministic predator–prey model. During the analysis of the deterministic model, it is shown that the system has saddle-node point of co-dimension 1, Hopf bifurcation and Bogdanov–Takens bifurcation of co-dimension 2. To study the effect of environmental fluctuation, we use perturbation to the birth rate of prey and death rate of predator density by Gaussian white noise. The persistence of the model and the stationary distribution is shown by forming a suitable Lyapunov function. Finally, numerical simulations are performed to validate the theoretical findings.

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来源期刊

Journal of Biological Systems 生物-生物学

CiteScore

2.80

自引率

12.50%

发文量

审稿时长

1 months

期刊介绍： The Journal of Biological Systems is published quarterly. The goal of the Journal is to promote interdisciplinary approaches in Biology and in Medicine, and the study of biological situations with a variety of tools, including mathematical and general systems methods. The Journal solicits original research papers and survey articles in areas that include (but are not limited to): Complex systems studies; isomorphies; nonlinear dynamics; entropy; mathematical tools and systems theories with applications in Biology and Medicine. Interdisciplinary approaches in Biology and Medicine; transfer of methods from one discipline to another; integration of biological levels, from atomic to molecular, macromolecular, cellular, and organic levels; animal biology; plant biology. Environmental studies; relationships between individuals, populations, communities and ecosystems; bioeconomics, management of renewable resources; hierarchy theory; integration of spatial and time scales. Evolutionary biology; co-evolutions; genetics and evolution; branching processes and phyllotaxis. Medical systems; physiology; cardiac modeling; computer models in Medicine; cancer research; epidemiology. Numerical simulations and computations; numerical study and analysis of biological data. Epistemology; history of science. The journal will also publish book reviews.