Global boundedness and asymptotic behavior of a predator-prey chemotaxis model with density-dependent motility and indirect signal production

Global boundedness and asymptotic behavior of a predator-prey chemotaxis model with density-dependent motility and indirect signal production | 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 Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 10 December 2025 V1 Latest version Share on Global boundedness and asymptotic behavior of a predator-prey chemotaxis model with density-dependent motility and indirect signal production Authors : Liangying Miao 0009-0007-6455-3762 [email protected] , Wenyi Teng , and xiaoyan gao 0009-0005-5532-535X Authors Info & Affiliations https://doi.org/10.22541/au.176534482.22695240/v1 145 views 155 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract This paper investigates the following predator-prey chemotaxis model with density-dependent motility and indirect signal production { u t = ∇ · ( d 1 ( z ) ∇ u ) + ∇ · ( χ 1 ( z ) u ∇ z ) + µ 1 u ( 1 − u − e 1 v ), x ∈ Ω, t > 0, v t = ∇ · ( d 2 ( z ) ∇ v ) − ∇ · ( χ 2 ( z ) v ∇ z ) + µ 2 v ( 1 + e 2 u − v ), x ∈ Ω, t > 0, w t = ∆ w − w + u + v, x ∈ Ω, t > 0, z t = ∆ z − z + w, x ∈ Ω, t > 0 under the homogeneous Neumann boundary conditions in a bounded smooth domain Ω ⊂ R n ( n ≥ 1 ), Here, µ 1, µ 2, e 1, e 2 ≥ 0 and the motility functions d i ( z ), χ i ( z ) ∈ C 2 [ 0, ∞ ] ( i = 1, 2 ) satisfy d i ( z ), χ i ( z ) > 0 for z ≥ 0 . For spatial dimension n =2, we establish the existence of globally bounded classical solution through a priori estimates and semigroup techniques. Furthermore, by constructing Lyapunov functionals, we analyze the asymptotic behavior of solution under specific parameter regimes: (i) If e 1 1, µ 2 is sufficiently large, then the solution ( u, v, w, z ) satisfying v ≥(≢)0 exponentially converges to the semi-trivial equilibrium point where only the predator persists; (iii) If e 1 = 1, µ 2 is sufficiently large, then the solution ( u, v, w, z ) converges algebraically the semi-trivial equilibrium point. Supplementary Material File (miao-teng-gao-mmas.pdf) Download 411.86 KB Information & Authors Information Version history V1 Version 1 10 December 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords density-dependent motility indirect signal production predator-prey stability uniform boundedness Authors Affiliations Liangying Miao 0009-0007-6455-3762 [email protected] Qinghai Nationalities University View all articles by this author Wenyi Teng Qinghai Nationalities University View all articles by this author xiaoyan gao 0009-0005-5532-535X Qinghai Nationalities University View all articles by this author Metrics & Citations Metrics Article Usage 145 views 155 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Liangying Miao, Wenyi Teng, xiaoyan gao. Global boundedness and asymptotic behavior of a predator-prey chemotaxis model with density-dependent motility and indirect signal production. Authorea . 10 December 2025. DOI: https://doi.org/10.22541/au.176534482.22695240/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. 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