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具有 Crowley-Martin 型反应函数的扩散型捕食-被捕食模型中 Allee 效应的时空行为影响。

Influence of Allee effect on the spatiotemporal behavior of a diffusive predator-prey model with Crowley-Martin type response function.

机构信息

Department of Mathematics, Visva-Bharati, Santiniketan, West Bengal, 731235, India.

Department of Mathematics, Krishna Chandra College, Hetampur, Birbhum, West Bengal, 731124, India.

出版信息

Sci Rep. 2023 Mar 22;13(1):4710. doi: 10.1038/s41598-023-28419-0.

DOI:10.1038/s41598-023-28419-0
PMID:36949110
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC10033644/
Abstract

The present paper is dealt with a predator-prey model in which the growth of the prey population is influenced by the Allee effect while the predator species are contended with the prey population following the Crowley-Martin type response function. The proposed model is comprehensively analyzed in terms of stability and manifestation of bifurcation of the system. The system unveils the bi-stability together with the existence of a separatrix. In view of the eminence of spatial ecology, the dynamical complexity emanating from the induction of the Allee effect in prey species of a Crowley-Martin reaction-diffusion predator-prey model is also investigated profoundly. The results of numerical simulations reveal that the present system dynamics is motivated by both the Allee effect and diffusion-controlled pattern formation growth to hot spots, stripe-hot spot mixtures, stripes, labyrinthine, stripe-cold spot mixtures, and cold spots replication. The theoretical consequences of the spatiotemporal model under study are validated through numerical simulations.

摘要

本文研究了一个捕食者-猎物模型，其中猎物种群的增长受到 Allee 效应的影响，而捕食物种则根据 Crowley-Martin 型反应函数与猎物种群竞争。从系统稳定性和分岔表现的角度对所提出的模型进行了全面分析。该模型揭示了双稳定性以及分隔线的存在。鉴于空间生态学的重要性，还深入研究了 Crowley-Martin 反应-扩散捕食者-猎物模型中引入 Allee 效应对猎物种群产生的动力复杂性。数值模拟结果表明，目前的系统动力学受到 Allee 效应和扩散控制的模式形成生长的共同驱动，形成热点、条纹-热点混合物、条纹、迷宫、条纹-冷点混合物和冷点复制。通过数值模拟验证了所研究时空模型的理论结果。

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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e00f/10033644/c6cbfff20f70/41598_2023_28419_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e00f/10033644/c789c49c130f/41598_2023_28419_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e00f/10033644/7fca8a4d62c1/41598_2023_28419_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e00f/10033644/4a5ff3b6d535/41598_2023_28419_Fig7_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e00f/10033644/87318a363502/41598_2023_28419_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e00f/10033644/3d486b4c2fb0/41598_2023_28419_Fig9_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e00f/10033644/83d593375fe5/41598_2023_28419_Fig10_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e00f/10033644/2162c43745ad/41598_2023_28419_Fig11_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e00f/10033644/2b88569ed0a9/41598_2023_28419_Fig12_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e00f/10033644/5c8908cccccb/41598_2023_28419_Fig13_HTML.jpg

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