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European Journal of Applied Mathematics最新文献

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Global dynamics and spatiotemporal heterogeneity of a preytaxis model with prey-induced acceleration 具有猎物诱导加速度的猎物大同模式的全局动力学和时空异质性
IF 1.9 4区 数学
European Journal of Applied Mathematics Pub Date : 2024-01-26 DOI: 10.1017/s0956792523000347
Chunlai Mu, Weirun Tao, Zhi-An Wang
{"title":"Global dynamics and spatiotemporal heterogeneity of a preytaxis model with prey-induced acceleration","authors":"Chunlai Mu, Weirun Tao, Zhi-An Wang","doi":"10.1017/s0956792523000347","DOIUrl":"https://doi.org/10.1017/s0956792523000347","url":null,"abstract":"Conventional preytaxis systems assume that prey-tactic velocity is proportional to the prey density gradient. However, many experiments exploring the predator–prey interactions show that it is the predator’s acceleration instead of velocity that is proportional to the prey density gradient in the prey-tactic movement, which we call preytaxis with prey-induced acceleration. Mathematical models of preytaxis with prey-induced acceleration were proposed by Arditi et al. ((2001) Theor. Popul. Biol. 59(3), 207–221) and Sapoukhina et al. ((2003) Am. Nat. 162(1), 61–76) to interpret the spatial heterogeneity of predators and prey observed in experiments. This paper is devoted to exploring the qualitative behaviour of such preytaxis systems with prey-induced acceleration and establishing the global existence of classical solutions with uniform-in-time bounds in all spatial dimensions. Moreover, we prove the global stability of spatially homogeneous prey-only and coexistence steady states with decay rates under certain conditions on system parameters. For the parameters outside the stability regime, we perform linear stability analysis to find the possible patterning regimes and use numerical simulations to demonstrate that spatially inhomogeneous time-periodic patterns will typically arise from the preytaxis system with prey-induced acceleration. Noticing that conventional preytaxis systems are unable to produce spatial patterns, our results imply that the preytaxis with prey-induced acceleration is indeed more appropriate than conventional preytaxis to interpret the spatial heterogeneity resulting from predator–prey interactions.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139587087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On degenerate reaction-diffusion epidemic models with mass action or standard incidence mechanism 关于具有质量作用或标准发生机制的退化反应-扩散流行病模型
IF 1.9 4区 数学
European Journal of Applied Mathematics Pub Date : 2024-01-22 DOI: 10.1017/s0956792523000359
Rachidi B. Salako, Yixiang Wu
{"title":"On degenerate reaction-diffusion epidemic models with mass action or standard incidence mechanism","authors":"Rachidi B. Salako, Yixiang Wu","doi":"10.1017/s0956792523000359","DOIUrl":"https://doi.org/10.1017/s0956792523000359","url":null,"abstract":"<p>In this paper, we consider reaction-diffusion epidemic models with mass action or standard incidence mechanism and study the impact of limiting population movement on disease transmissions. We set either the dispersal rate of the susceptible or infected people to zero and study the corresponding degenerate reaction-diffusion model. Our main approach to study the global dynamics of these models is to construct delicate Lyapunov functions. Our results show that the consequences of limiting the movement of susceptible or infected people depend on transmission mechanisms, model parameters and population size.</p>","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139516923","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The fully parabolic multi-species chemotaxis system in 中的全抛物线多物种趋化系统
IF 1.9 4区 数学
European Journal of Applied Mathematics Pub Date : 2024-01-19 DOI: 10.1017/s0956792523000372
Ke Lin
{"title":"The fully parabolic multi-species chemotaxis system in","authors":"Ke Lin","doi":"10.1017/s0956792523000372","DOIUrl":"https://doi.org/10.1017/s0956792523000372","url":null,"abstract":"<p>This article is devoted to the analysis of the parabolic–parabolic chemotaxis system with multi-components over <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240118130640071-0186:S0956792523000372:S0956792523000372_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$mathbb{R}^2$</span></span></img></span></span>. The optimal small initial condition on the global existence of solutions for multi-species chemotaxis model in the fully parabolic situation had not been attained as far as the author knows. In this paper, we prove that under the sub-critical mass condition, any solutions to conflict-free system exist globally. Moreover, the global existence of solutions to system with strong self-repelling effect has been discussed even for large initial data. The proof is based on the modified free energy functional and the Moser–Trudinger inequality for system.</p>","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139495908","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Recurrent and chaotic outbreaks in SIR model SIR 模型中的反复和混乱爆发
IF 1.9 4区 数学
European Journal of Applied Mathematics Pub Date : 2024-01-18 DOI: 10.1017/s0956792523000360
Chunyi Gai, Theodore Kolokolnikov, Jan Schrader, Vedant Sharma
{"title":"Recurrent and chaotic outbreaks in SIR model","authors":"Chunyi Gai, Theodore Kolokolnikov, Jan Schrader, Vedant Sharma","doi":"10.1017/s0956792523000360","DOIUrl":"https://doi.org/10.1017/s0956792523000360","url":null,"abstract":"We examine several extensions to the basic Susceptible-Infected-Recovered model, which are able to induce recurrent outbreaks (the basic Susceptible-Infected-Recovered model by itself does not exhibit recurrent outbreaks). We first analyse how slow seasonal variations can destabilise the endemic equilibrium, leading to recurrent outbreaks. In the limit of slow immunity loss, we derive asymptotic thresholds that characterise this transition. In the outbreak regime, we use asymptotic matching to obtain a two-dimensional discrete map which describes outbreak times and strength. We then analyse the resulting map using linear stability and numerics. As the frequency of forcing is increased, the map exhibits a period-doubling route to chaos which alternates with periodic outbreaks of increasing frequency. Other extensions that can lead to recurrent outbreaks include the addition of noise, state-dependent variation and fine-graining of model classes.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139501566","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Absolute concentration robustness and multistationarity in reaction networks: Conditions for coexistence 反应网络中的绝对浓度稳健性和多稳定性：共存的条件
IF 1.9 4区 数学
European Journal of Applied Mathematics Pub Date : 2024-01-02 DOI: 10.1017/s0956792523000335
Nidhi Kaihnsa, Tung Nguyen, Anne Shiu
{"title":"Absolute concentration robustness and multistationarity in reaction networks: Conditions for coexistence","authors":"Nidhi Kaihnsa, Tung Nguyen, Anne Shiu","doi":"10.1017/s0956792523000335","DOIUrl":"https://doi.org/10.1017/s0956792523000335","url":null,"abstract":"<p>Many reaction networks arising in applications are multistationary, that is, they have the capacity for more than one steady state, while some networks exhibit absolute concentration robustness (ACR), which means that some species concentration is the same at all steady states. Both multistationarity and ACR are significant in biological settings, but only recently has attention focused on the possibility for these properties to coexist. Our main result states that such coexistence in at-most-bimolecular networks (which encompass most networks arising in biology) requires at least three species, five complexes and three reactions. We prove additional bounds on the number of reactions for general networks based on the number of linear conservation laws. Finally, we prove that, outside of a few exceptional cases, ACR is equivalent to non-multistationarity for bimolecular networks that are small (more precisely, one-dimensional or up to two species). Our proofs involve analyses of systems of sparse polynomials, and we also use classical results from chemical reaction network theory.</p>","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139077366","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Variational inequalities arising from credit rating migration with buffer zone 有缓冲区的信用评级迁移所产生的变量不等式
IF 1.9 4区 数学
European Journal of Applied Mathematics Pub Date : 2023-12-14 DOI: 10.1017/s095679252300030x
Xinfu Chen, Jin Liang
{"title":"Variational inequalities arising from credit rating migration with buffer zone","authors":"Xinfu Chen, Jin Liang","doi":"10.1017/s095679252300030x","DOIUrl":"https://doi.org/10.1017/s095679252300030x","url":null,"abstract":"<p>In Chen and Liang previous work, a model, together with its well-posedness, was established for credit rating migrations with different upgrade and downgrade thresholds (i.e. a buffer zone, also called dead band in engineering). When positive dividends are introduced, the model in Chen and Liang (<span>SIAM Financ. Math.</span> 12, 941–966, 2021) may not be well-posed. Here, in this paper, a new model is proposed to include the realistic nonzero dividend scenarios. The key feature of the new model is that partial differential equations in Chen and Liang (<span>SIAM Financ. Math.</span> 12, 941–966, 2021) are replaced by variational inequalities, thereby creating a new free boundary, besides the original upgrading and downgrading free boundaries. Well-posedness of the new model, together with a few financially meaningful properties, is established. In particular, it is shown that when time to debt paying deadline is long enough, the underlying dividend paying company is always in high grade rating, that is, only when time to debt paying deadline is within a certain range, there can be seen the phenomenon of credit rating migration.</p>","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138627865","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Analysis and numerical simulations of travelling waves due to plant–soil negative feedback 植物-土壤负反馈引起的行波分析与数值模拟
IF 1.9 4区 数学
European Journal of Applied Mathematics Pub Date : 2023-12-07 DOI: 10.1017/s0956792523000323
Annalisa Iuorio, Nicole Salvatori, Gerardo Toraldo, Francesco Giannino
{"title":"Analysis and numerical simulations of travelling waves due to plant–soil negative feedback","authors":"Annalisa Iuorio, Nicole Salvatori, Gerardo Toraldo, Francesco Giannino","doi":"10.1017/s0956792523000323","DOIUrl":"https://doi.org/10.1017/s0956792523000323","url":null,"abstract":"In this work, we carry out an analytical and numerical investigation of travelling waves representing arced vegetation patterns on sloped terrains. These patterns are reported to appear also in ecosystems which are not water deprived; therefore, we study the hypothesis that their appearance is due to plant–soil negative feedback, namely due to biomass-(auto)toxicity interactions. To this aim, we introduce a reaction-diffusion-advection model describing the dynamics of vegetation biomass and toxicity which includes the effect of sloped terrains on the spatial distribution of these variables. Our analytical investigation shows the absence of Turing patterns, whereas travelling waves (moving uphill in the slope direction) emerge. Investigating the corresponding dispersion relation, we provide an analytic expression for the asymptotic speed of the wave. Numerical simulations not only just confirm this analytical quantity but also reveal the impact of toxicity on the structure of the emerging travelling pattern. Our analysis represents a further step in understanding the mechanisms behind relevant plants‘ spatial distributions observed in real life. In particular, since vegetation patterns (both stationary and transient) are known to play a crucial role in determining the underlying ecosystems’ resilience, the framework presented here allows us to better understand the emergence of such structures to a larger variety of ecological scenarios and hence improve the relative strategies to ensure the ecosystems’ resilience.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138579176","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Propagation dynamics of a mutualistic model of mistletoes and birds with nonlocal dispersal 具有非局部扩散的槲寄生与鸟类共生模式的繁殖动力学
IF 1.9 4区 数学
European Journal of Applied Mathematics Pub Date : 2023-12-04 DOI: 10.1017/s0956792523000311
Juan He, Guo-Bao Zhang, Ting Liu
{"title":"Propagation dynamics of a mutualistic model of mistletoes and birds with nonlocal dispersal","authors":"Juan He, Guo-Bao Zhang, Ting Liu","doi":"10.1017/s0956792523000311","DOIUrl":"https://doi.org/10.1017/s0956792523000311","url":null,"abstract":"This paper is devoted to the study of the propagation dynamics of a mutualistic model of mistletoes and birds with nonlocal dispersal. By applying the theory of asymptotic speeds of spread and travelling waves for monotone semiflows, we establish the existence of the asymptotic spreading speed <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0956792523000311_inline1.png\" /> <jats:tex-math> $c^*$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, the existence of travelling wavefronts with the wave speed <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0956792523000311_inline2.png\" /> <jats:tex-math> $cge c^*$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> and the nonexistence of travelling wavefronts with <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0956792523000311_inline3.png\" /> <jats:tex-math> $clt c^*$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. It turns out that the spreading speed coincides with the minimal wave speed of travelling wavefronts. Moreover, some lower and upper bound estimates of the spreading speed <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0956792523000311_inline4.png\" /> <jats:tex-math> $c^*$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> are provided.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138539695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Propagation dynamics of a mutualistic model of mistletoes and birds with nonlocal dispersal 具有非局部扩散的槲寄生与鸟类共生模式的繁殖动力学
IF 1.9 4区 数学
European Journal of Applied Mathematics Pub Date : 2023-12-04 DOI: 10.1017/s0956792523000311
Juan He, Guo-Bao Zhang, Ting Liu
{"title":"Propagation dynamics of a mutualistic model of mistletoes and birds with nonlocal dispersal","authors":"Juan He, Guo-Bao Zhang, Ting Liu","doi":"10.1017/s0956792523000311","DOIUrl":"https://doi.org/10.1017/s0956792523000311","url":null,"abstract":"This paper is devoted to the study of the propagation dynamics of a mutualistic model of mistletoes and birds with nonlocal dispersal. By applying the theory of asymptotic speeds of spread and travelling waves for monotone semiflows, we establish the existence of the asymptotic spreading speed <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0956792523000311_inline1.png\" /> <jats:tex-math> $c^*$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, the existence of travelling wavefronts with the wave speed <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0956792523000311_inline2.png\" /> <jats:tex-math> $cge c^*$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> and the nonexistence of travelling wavefronts with <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0956792523000311_inline3.png\" /> <jats:tex-math> $clt c^*$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. It turns out that the spreading speed coincides with the minimal wave speed of travelling wavefronts. Moreover, some lower and upper bound estimates of the spreading speed <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0956792523000311_inline4.png\" /> <jats:tex-math> $c^*$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> are provided.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138539699","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Leveraging memory effects and gradient information in consensus-based optimisation: On global convergence in mean-field law 在基于共识的优化中利用记忆效应和梯度信息:关于平均场律的全局收敛
4区 数学
European Journal of Applied Mathematics Pub Date : 2023-10-20 DOI: 10.1017/s0956792523000293
Konstantin Riedl
{"title":"Leveraging memory effects and gradient information in consensus-based optimisation: On global convergence in mean-field law","authors":"Konstantin Riedl","doi":"10.1017/s0956792523000293","DOIUrl":"https://doi.org/10.1017/s0956792523000293","url":null,"abstract":"Abstract In this paper, we study consensus-based optimisation (CBO), a versatile, flexible and customisable optimisation method suitable for performing nonconvex and nonsmooth global optimisations in high dimensions. CBO is a multi-particle metaheuristic, which is effective in various applications and at the same time amenable to theoretical analysis thanks to its minimalistic design. The underlying dynamics, however, is flexible enough to incorporate different mechanisms widely used in evolutionary computation and machine learning, as we show by analysing a variant of CBO which makes use of memory effects and gradient information. We rigorously prove that this dynamics converges to a global minimiser of the objective function in mean-field law for a vast class of functions under minimal assumptions on the initialisation of the method. The proof in particular reveals how to leverage further, in some applications advantageous, forces in the dynamics without loosing provable global convergence. To demonstrate the benefit of the herein investigated memory effects and gradient information in certain applications, we present numerical evidence for the superiority of this CBO variant in applications such as machine learning and compressed sensing, which en passant widen the scope of applications of CBO.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135617449","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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