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Mathematical Modelling of Natural Phenomena最新文献

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Mathematical modelling in nonlocal Mindlin’s strain gradient thermoelasticity with voids 带孔洞的非局部Mindlin应变梯度热弹性的数学建模
IF 2.2 4区 数学
Mathematical Modelling of Natural Phenomena Pub Date : 2022-09-14 DOI: 10.1051/mmnp/2022042
M. Aouadi
{"title":"Mathematical modelling in nonlocal Mindlin’s strain gradient thermoelasticity with voids","authors":"M. Aouadi","doi":"10.1051/mmnp/2022042","DOIUrl":"https://doi.org/10.1051/mmnp/2022042","url":null,"abstract":"A nonlocal theory for thermoelastic materials with voids based on Mindlin’s strain gradient theory was derived in this paper with some qualitative properties. We have also established the size effect of nonlocal heat conduction with the aids of extended irreversible thermodynamics and generalized free energy. The obtained system of equations is a coupling of three equations with higher gradients terms due to the length scale parameters ϖ and l . This poses some new mathematical difficulties due to the lack of regularity. Based on nonlinear semigroups and the theory of monotone operators, we establish existence and uniqueness of weak and strong solutions to the one dimensional problem. By an approach based on the Gearhart-HerbstPrüss-Huang theorem, we prove that the associated semigroup is exponentially stable; but not analytic.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2022-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44488418","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 normal velocity of the population front in the "predator-prey" model “捕食者-猎物”模型中种群前沿的法向速度
IF 2.2 4区 数学
Mathematical Modelling of Natural Phenomena Pub Date : 2022-08-18 DOI: 10.1051/mmnp/2022039
Evgeniy Dats, Sergey Minaev, Vladimir Gubernov, Junnosuke Okajima
{"title":"The normal velocity of the population front in the \"predator-prey\" model","authors":"Evgeniy Dats, Sergey Minaev, Vladimir Gubernov, Junnosuke Okajima","doi":"10.1051/mmnp/2022039","DOIUrl":"https://doi.org/10.1051/mmnp/2022039","url":null,"abstract":"The propagation of one and two-dimensional waves of populations are numerically investigated in the framework of the ``predator-prey'' model with the Arditi - Ginzburg trophic function. The propagation of prey and predator population waves and the propagation of co-existing populations' waves are considered. The simulations demonstrate that even in the case of an unstable quasi-equilibrium state of the system, which is established behind the front of a traveling wave, the propagation velocity of the joint population wave is a well-defined function. The calculated average propagation velocity of a cellular non-stationary wave front is determined uniquely for a given set of problem parameters.  The estimations of the wave propagation velocity are obtained for both the case of a plane and cellular wave fronts of populations. The structure and velocity of outward propagating circular cellular wave are investigated to clarify the local curvature and scaling effects on the wave dynamics.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2022-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48741916","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
Controllability of Delayed Discret Fornasini-Marchesini Model via Quantization and Random Packet Dropouts 基于量化和随机丢包的延迟离散Fornasini-Marchesini模型的可控性
IF 2.2 4区 数学
Mathematical Modelling of Natural Phenomena Pub Date : 2022-08-17 DOI: 10.1051/mmnp/2022040
Adnen Adnen
{"title":"Controllability of Delayed Discret Fornasini-Marchesini Model via Quantization and Random Packet Dropouts","authors":"Adnen Adnen","doi":"10.1051/mmnp/2022040","DOIUrl":"https://doi.org/10.1051/mmnp/2022040","url":null,"abstract":"This research is devoted to Fornasnisi-Marchesini model (FM). More precisely, the investigation of the control problem for the second model discrete-time FM. Random packet dropouts, time delays and quantization are taken into consideration in the feedback control problem simultaneously. Measured signals are quantized before being communicated. A logarithmic quantizer is utilized and quantized signal measurements are handled by a sector bound method. The random packet dropouts are modeled as a Bernoulli process. A control law model which depends on packet dropouts and quantization is formulated. Notably, we lighten the assumptions by using the Schur complement. Besides, both a state feedback controller and an observer-based output feedback controller are designed to ensure corresponding closed-loop systems asymptotically stability. Sufficient conditions on mean square asymptotic stability in terms of LMIs have been obtained. Finally, two numerical example show the feasibility of our theoretical results.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2022-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48083437","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: 3
Stochastic bifurcations and tipping phenomena of insect outbreak systems driven by α-stable Lévy processes α-稳定Lévy过程驱动的昆虫爆发系统的随机分叉和倾翻现象
IF 2.2 4区 数学
Mathematical Modelling of Natural Phenomena Pub Date : 2022-08-08 DOI: 10.1051/mmnp/2022037
S. Yuan, Yang Li, Zhigang Zeng
{"title":"Stochastic bifurcations and tipping phenomena of insect outbreak systems driven by α-stable Lévy processes","authors":"S. Yuan, Yang Li, Zhigang Zeng","doi":"10.1051/mmnp/2022037","DOIUrl":"https://doi.org/10.1051/mmnp/2022037","url":null,"abstract":"In this work, we mainly characterize stochastic bifurcations and tipping phenomena of insect outbreak dynamical systems driven by $alpha$-stable L'evy processes. In one-dimensional insect outbreak model, we find the fixed points representing refuge and outbreak from the bifurcation curves, and carry out a sensitivity analysis with respect to small changes in the model parameters, the stability index and the noise intensity. We perform the numerical simulations of dynamical trajectories using Monte Carlo methods, which contribute to looking at stochastic hysteresis phenomenon. As for two-dimensional insect outbreak system, we identify the global stability properties of fixed points and  express the probability density function by the stationary solution of the nonlocal Fokker-Planck equation. Through numerical modelling,  the phase portrait makes it possible to detect critical transitions among the stable states. It is then worth describing stochastic bifurcation associated with tipping points induced by noise through a careful examination of the dynamical paths of the insect outbreak system with external forcing. The results give new insight into the sensitivity of ecosystems to realistic environmental changes represented by stochastic perturbations.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":"46 4","pages":""},"PeriodicalIF":2.2,"publicationDate":"2022-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41259543","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: 3
Optimal control for a bone metastasis with radiotherapy model using a linear objective functional 利用线性目标泛函的放射治疗模型对骨转移进行最优控制
IF 2.2 4区 数学
Mathematical Modelling of Natural Phenomena Pub Date : 2022-08-07 DOI: 10.1051/mmnp/2022038
Ariel Camacho, Enrique Diaz-Ocampo, S. Jerez
{"title":"Optimal control for a bone metastasis with radiotherapy model using a linear objective functional","authors":"Ariel Camacho, Enrique Diaz-Ocampo, S. Jerez","doi":"10.1051/mmnp/2022038","DOIUrl":"https://doi.org/10.1051/mmnp/2022038","url":null,"abstract":"Radiation is known to cause genetic damage to highly proliferative cells such as cancer cells. However, the radiotherapy effects  to  bone cells is not completely known. In this work we present a mathematical modeling framework to test hypotheses related to the radiation-induced effects on bone metastasis. Thus, we pose an optimal control problem based  on a Komarova model describing the interactions between cancer cells and  bone cells   at a single site of bone remodeling.  The radiotherapy treatment  is included in the form of a functional which   minimizes the use of radiation using a penalty function. Moreover, we are interested to model the 'on' and the 'off' time states of the radiation schedules;  so we propose an optimal control problem with a L1-type objective functional.\u0000\u0000Bang-bang or singular arc solutions are the  obtained optimal control solutions. We characterize both solutions types   and explicitly give necessary optimality conditions for them. We present numerical simulations to analyze the different possible radiation effects on the bone and cancer cells. We also evaluate  the more significant parameters to shift from a bang-bang solution to a singular arc solution and vice versa. Additionally, we study a fractionated radiotherapy model.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2022-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47394342","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: 2
Editorial 编辑
IF 2.2 4区 数学
Mathematical Modelling of Natural Phenomena Pub Date : 2022-08-04 DOI: 10.1051/mmnp/2022036
A. Ruimy, Vitaly Volpert
{"title":"Editorial","authors":"A. Ruimy, Vitaly Volpert","doi":"10.1051/mmnp/2022036","DOIUrl":"https://doi.org/10.1051/mmnp/2022036","url":null,"abstract":"","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2022-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48766732","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: 1
DEGREE-BIASED ADVECTION-DIFFUSION ON UNDIRECTED GRAPHS/NETWORKS 无向图/网络上的度偏平流扩散
IF 2.2 4区 数学
Mathematical Modelling of Natural Phenomena Pub Date : 2022-08-01 DOI: 10.1051/mmnp/2022034
E. Estrada, Manuel Miranda
{"title":"DEGREE-BIASED ADVECTION-DIFFUSION ON UNDIRECTED GRAPHS/NETWORKS","authors":"E. Estrada, Manuel Miranda","doi":"10.1051/mmnp/2022034","DOIUrl":"https://doi.org/10.1051/mmnp/2022034","url":null,"abstract":"There are several phenomena in nature governed by simultaneous or intermittent diffusion and advection processes. Many of these systems are networked by their own nature. Here we propose a degree-biased advection processes to undirected networks. For that purpose we define and study the degree-biased advection operator. We then develop a degree-biased advection-diffusion equation on networks and study its general properties. We give computational evidence of the utility of this new model by studying random graphs as well as a real-life patched landscape network in southern Madagascar. In the last case we show that the foraging movement of the species L. catta in this environment occurs mainly in a diffusive way with important contributions of advective motions in agreement with previous empirical observations.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46166069","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: 1
Modelling optimal pest control of non-autonomous predator-prey interaction 非自治捕食-被捕食相互作用下害虫最优控制模型
IF 2.2 4区 数学
Mathematical Modelling of Natural Phenomena Pub Date : 2022-07-26 DOI: 10.1051/mmnp/2022033
Paulo Jorge dos Santos Pinto Rebelo, Silvério Simões Rosa, César Augusto Simões Teixeira Marques da Silva
{"title":"Modelling optimal pest control of non-autonomous predator-prey interaction","authors":"Paulo Jorge dos Santos Pinto Rebelo, Silvério Simões Rosa, César Augusto Simões Teixeira Marques da Silva","doi":"10.1051/mmnp/2022033","DOIUrl":"https://doi.org/10.1051/mmnp/2022033","url":null,"abstract":"An ecological system comprehended by a pest and  its natural enemy, the predator, is considered. Parameters of system are time dependent in order to accompany their variations associated to climate evolutions. Combining the use of pesticides and of extra supply of food to predators,  we propose the eradication of pest through optimal control having those two measures as controls. Is established that the resulting problem has a unique solution. Uniqueness is obtained on the whole interval using a  recursive argument. The usefulness of model to tackle the pest population is backed by numerical simulation results.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2022-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42777637","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
Analytical detection of stationary Turing pattern in a predator-prey system with generalist predator 广义捕食者捕食系统中平稳图灵模式的分析检测
IF 2.2 4区 数学
Mathematical Modelling of Natural Phenomena Pub Date : 2022-07-22 DOI: 10.1051/mmnp/2022032
Subrata Dey, M. Banerjee, S. Ghorai
{"title":"Analytical detection of stationary Turing pattern in a predator-prey system with generalist predator","authors":"Subrata Dey, M. Banerjee, S. Ghorai","doi":"10.1051/mmnp/2022032","DOIUrl":"https://doi.org/10.1051/mmnp/2022032","url":null,"abstract":"A prey-predator model with prey dependent Holling type-II functional response and a generalist predator exhibits complex dynamics in response to parameter variation. Generalist predators implicitly exploiting multiple food resources reduce predation pressure on their focal prey species that causes it to become more stable compared to a prey-predator system with specialist predator. In the temporal system, bistability and tristability are observed along with various global and local bifurcations. Existence of homogeneous and heterogeneous positive steady state solutions are shown to exist for suitable ranges of parameter values in the spatiotemporal diffusive system. Weakly nonlinear analysis using multi-scale perturbation technique is employed to derive amplitude equation for the stationary patterns near the Turing bifurcation threshold. The analytical results of the amplitude equations are validated using numerical simulations. We also identify bifurcation of multiple stable stationary patch solutions as well as dynamic pattern solution for parameter values in the Turing and Turing-Hopf regions.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2022-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48805153","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: 4
Optimal multiplicative control of bacterial quorum sensing under external enzyme impact 外部酶作用下细菌群体感应的最优乘法控制
IF 2.2 4区 数学
Mathematical Modelling of Natural Phenomena Pub Date : 2022-07-21 DOI: 10.1051/mmnp/2022031
A. Maslovskaya, C. Kuttler, A. Chebotarev, A. Kovtanyuk
{"title":"Optimal multiplicative control of bacterial quorum sensing under external enzyme impact","authors":"A. Maslovskaya, C. Kuttler, A. Chebotarev, A. Kovtanyuk","doi":"10.1051/mmnp/2022031","DOIUrl":"https://doi.org/10.1051/mmnp/2022031","url":null,"abstract":"The use of external enzymes provides an alternative way of reducing communication in pathogenic bacteria that may lead to the degradation of their signal and the loss of their pathogeneity. The present study considers an optimal control problem for the semilinear reaction-diffusion model of bacterial quorum sensing under the impact of external enzymes. Estimates of the solution of the controlled system are obtained, on the basis of which the solvability of the extremal problem is proved and the necessary optimality conditions of the first-order are derived. A numerical algorithm to find a solution of the optimal control problem is constructed and implemented. The conducted numerical experiments demonstrate an opportunity to build an effective strategy of the enzymes impact for treatment.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2022-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47182272","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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