Qualitative analysis of Turing bifurcation in a diffusion population model with environmental toxin threat and Allee effect

Qualitative analysis of Turing bifurcation in a diffusion population model with environmental toxin threat and Allee effect | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL Mathematical Methods in the Applied Sciences This is a preprint and has not been peer reviewed. Data may be preliminary. 15 September 2025 V1 Latest version Share on Qualitative analysis of Turing bifurcation in a diffusion population model with environmental toxin threat and Allee effect Authors : Meng Gao , Haisong Cao , Jianfeng Jiao 0000-0002-9722-9623 [email protected] , and Hongcui Chang Authors Info & Affiliations https://doi.org/10.22541/au.175793624.49650546/v1 Published Mathematical Methods in the Applied Sciences Version of record Peer review timeline 237 views 163 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract In this paper, the spatiotemporal pattern dynamics of a diffusion population model with Allee effect and environmental toxins is considered. Firstly, the boundedness and positivity of the system are proved, the existence and stability of the equilibrium are analyzed, and the conditions of the occurrence of Turing bifurcation are deduced. Subsequently, the mechanism for the selection of patterns around the positive equilibrium was provided through weakly nonlinear analysis. One finds that weak Allee effect can restore the reduction of population density and undergoes the bistable phenomena. Environmental toxins can lead to Hopf bifurcation and saddle-node bifurcation, and change the topology of the system. Self-diffusion can induce Turing bifurcation, and the hexagonal hole patterns, mixed patterns of holes and stripes, and striped patterns are shown. Finally, theoretical results are validated through numerical simulations. These findings provide a scientific basis for population conservation strategies under the threat of environmental toxins. Supplementary Material File (main document -latex pdf.pdf) Download 2.85 MB Information & Authors Information Version history V1 Version 1 15 September 2025 Peer review timeline Published Mathematical Methods in the Applied Sciences Version of Record 12 Mar 2026 Published Copyright This work is licensed under a Non Exclusive No Reuse License. Collection Mathematical Methods in the Applied Sciences Keywords allee effect environmental toxin population model self-diffusion turing bifurcation Authors Affiliations Meng Gao North China University of Water Resources and Electric Power View all articles by this author Haisong Cao North China University of Water Resources and Electric Power View all articles by this author Jianfeng Jiao 0000-0002-9722-9623 [email protected] Zhengzhou University of Aeronautics View all articles by this author Hongcui Chang Zhengzhou University of Aeronautics View all articles by this author Metrics & Citations Metrics Article Usage 237 views 163 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Meng Gao, Haisong Cao, Jianfeng Jiao, et al. Qualitative analysis of Turing bifurcation in a diffusion population model with environmental toxin threat and Allee effect. Authorea . 15 September 2025. DOI: https://doi.org/10.22541/au.175793624.49650546/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . Format Please select one from the list RIS (ProCite, Reference Manager) EndNote BibTex Medlars RefWorks Direct import Tips for downloading citations document.getElementById('citMgrHelpLink').addEventListener('click', function() { popupHelp(this.href); return false; }); $(".js__slcInclude").on("change", function(e){ if ($(this).val() == 'refworks') $('#direct').prop("checked", false); $('#direct').prop("disabled", ($(this).val() == 'refworks')); }); View Options View options PDF View PDF Figures Tables Media Share Share Share article link Copy Link Copied! Copying failed. 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