Subdural ECoG data recorded from the matrix of electrodes during syllable pronunciation are analyzed by the method of circular-linear regression. Phase waves in 1D electrode arrays and in the whole 2D set of electrodes are detected, and their spatial organization and temporal evolution are studied. Phase portraits of wave vectors indicate the presence of sources, sinks, and saddle points. The analysis of temporal evolution of phase portraits shows that they changed more at the beginning of syllable pronunciation. Furthermore, wave sources were more stable in their localization during the pronunciation. Overall, in spite of large variability of phase portraits, they represent some characterization of the dynamics of electric potential in the cerebral cortex.
{"title":"Analysis of phase waves in the ECoG data","authors":"Alexandre Aksenov, A. Beuter","doi":"10.1051/mmnp/2021045","DOIUrl":"https://doi.org/10.1051/mmnp/2021045","url":null,"abstract":"Subdural ECoG data recorded from the matrix of electrodes during syllable pronunciation are analyzed by the method of circular-linear regression. Phase waves in 1D electrode arrays and in the whole 2D set of electrodes are detected, and their spatial organization and temporal evolution are studied. Phase portraits of wave vectors indicate the presence of sources, sinks, and saddle points. The analysis of temporal evolution of phase portraits shows that they changed more at the beginning of syllable pronunciation. Furthermore, wave sources were more stable in their localization during the pronunciation. Overall, in spite of large variability of phase portraits, they represent some characterization of the dynamics of electric potential in the cerebral cortex.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2021-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48952369","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}
In our model of the COVID-19 epidemic, infected individuals can be of four types, according whether they are asymptomatic ($A$) or symptomatic ($I$), and use a contact tracing mobile phone app ($Y$) or not ($N$). We denote by $f$ the fraction of $A$'s, by $y$ the fraction of $Y$'s and by $R_0$ the average number of secondary infections from a random infected individual. We investigate the effect of non-digital interventions and of digital interventions, depending on the willingness to quarantine, parameterized by four cooperating probabilities. For a given `effective' $R_0$ obtained with non-digital interventions, we use non-negative matrix theory and stopping line techniques to characterize mathematically the minimal fraction $y_0$ of app users needed to curb the epidemic. We show that under a wide range of scenarios, the threshold $y_0$ as a function of $R_0$ rises steeply from 0 at $R_0=1$ to prohibitively large values (of the order of $60-70%$ up) whenever $R_0$ is above 1.3. Our results show that moderate rates of adoption of a contact tracing app can reduce $R_0$ but are by no means sufficient to reduce it below 1 unless it is already very close to 1 thanks to non-digital interventions.
{"title":"A mathematical assessment of the efficiency of quarantining and contact tracing in curbing the COVID-19 epidemic","authors":"A. Lambert","doi":"10.1051/mmnp/2021042","DOIUrl":"https://doi.org/10.1051/mmnp/2021042","url":null,"abstract":"In our model of the COVID-19 epidemic, infected individuals can be of four types, according whether they are asymptomatic ($A$) or symptomatic ($I$), and use a contact tracing mobile phone app ($Y$) or not ($N$). We denote by $f$ the fraction of $A$'s, by $y$ the fraction of $Y$'s and by $R_0$ the average number of secondary infections from a random infected individual.\u0000We investigate the effect of non-digital interventions and of digital interventions, depending on the willingness to quarantine, parameterized by four cooperating probabilities.\u0000For a given `effective' $R_0$ obtained with non-digital interventions, we use non-negative matrix theory and stopping line techniques to characterize mathematically the minimal fraction $y_0$ of app users needed to curb the epidemic. We show that under a wide range of scenarios, the threshold $y_0$ as a function of $R_0$ rises steeply from 0 at $R_0=1$ to prohibitively large values (of the order of $60-70%$ up) whenever $R_0$ is above 1.3. Our results show that moderate rates of adoption of a contact tracing app can reduce $R_0$ but are by no means sufficient to reduce it below 1 unless it is already very close to 1 thanks to non-digital interventions.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2021-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46407584","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}
K. Shah, M. Arfan, Meshal Shutaywi, Wejdan Deebani, Dumitru Balaneau
The given article is devoted to presentation of some results regarding existence and uniqueness of solution to a fractional order model that addressing the effect of immigration on the transmission dynamics of a population model. Further, in view of this investigation the effect of immigration have been checked on transmission of recent pandemic known as Corona virus COVID-19. The concerned results have been established by using fixed point theory approach. After investigation qualitative analysis of the considered model, by applying Laplace transform along with decomposition method, we have calculated some series type results for the concerned model. The unknown quantities of each equation have been decomposed into small quantities to calculate each small quantity very easily for the series solution by adding first few terms of the said quantities. Approximate results of some testing data with different cases are given to illustrate the results.
{"title":"Investigation of COVID-19 Mathematical Model Under Fractional Order Derivative","authors":"K. Shah, M. Arfan, Meshal Shutaywi, Wejdan Deebani, Dumitru Balaneau","doi":"10.1051/mmnp/2021044","DOIUrl":"https://doi.org/10.1051/mmnp/2021044","url":null,"abstract":"The given article is devoted to presentation of some results regarding existence and uniqueness of solution to a fractional order model that addressing the effect of immigration on the transmission dynamics of a population model. Further, in view of this investigation the effect of immigration have been checked on transmission of recent pandemic known as Corona virus COVID-19. The concerned results have been established by using fixed point theory approach. After investigation qualitative analysis of the considered model, by applying Laplace transform along with decomposition method, we have calculated some series type results for the concerned model. The unknown quantities of each equation have been decomposed into small quantities to calculate each small quantity very easily for the series solution by adding first few terms of the said quantities. Approximate results of some testing data with different cases are given to illustrate the results.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2021-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42301673","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}
The current paper is devoted to stochastic damped higher order KdV equation driven by Poisson process. We establish the well-posedness of stochastic damped higher-order KdV equation, and prove that there exists an unique invariant measure for non-random initial conditions. Some discussion on the general pure jump noise case are also provided. Some numerical simulations of the invariant measure are provided to support the theoretical results. Mathematics Subject Classification. 60H15, 37L55. Received March 27, 2020. Accepted July 13, 2021.
{"title":"Invariant measure of stochastic higher order KdV equation driven by Poisson processes","authors":"Pengfei Xu, Jianhua Huang, Wei Yan","doi":"10.1051/MMNP/2021041","DOIUrl":"https://doi.org/10.1051/MMNP/2021041","url":null,"abstract":"The current paper is devoted to stochastic damped higher order KdV equation driven by Poisson process. We establish the well-posedness of stochastic damped higher-order KdV equation, and prove that there exists an unique invariant measure for non-random initial conditions. Some discussion on the general pure jump noise case are also provided. Some numerical simulations of the invariant measure are provided to support the theoretical results. Mathematics Subject Classification. 60H15, 37L55. Received March 27, 2020. Accepted July 13, 2021.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2021-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43425632","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}
Pub Date : 2021-07-03DOI: 10.22541/AU.162531612.21576519/V1
Kalyan Manna, M. Banerjee
Generalist predators exploit multiple food sources and it is economical for them to reduce predation pressure on a particular prey species when their density level becomes comparatively less. As a result, a prey-predator system tends to become more stable in the presence of a generalist predator. In this article, we investigate the roles of both the diffusion and nonlocal prey consumption in shaping the population distributions for interacting generalist predator and its focal prey species. In this regard, we first derive the conditions associated with Turing instability through linear analysis. Then, we perform a weakly nonlinear analysis and derive a cubic Stuart-Landau equation governing amplitude of the resulting patterns near Turing bifurcation boundary. Further, we present a wide variety of numerical simulations to corroborate our analytical findings as well as to illustrate some other complex spatiotemporal dynamics. Interestingly, our study reveals the existence of traveling wave solutions connecting two spatially homogeneous coexistence steady states in Turing domain under the influence of temporal bistability phenomenon. Also, our investigation shows that nonlocal prey consumption acts as a stabilizing force for the system dynamics.
{"title":"Spatiotemporal pattern formation in a prey-predator model with generalist predator","authors":"Kalyan Manna, M. Banerjee","doi":"10.22541/AU.162531612.21576519/V1","DOIUrl":"https://doi.org/10.22541/AU.162531612.21576519/V1","url":null,"abstract":"Generalist predators exploit multiple food sources and it is economical\u0000for them to reduce predation pressure on a particular prey species when\u0000their density level becomes comparatively less. As a result, a\u0000prey-predator system tends to become more stable in the presence of a\u0000generalist predator. In this article, we investigate the roles of both\u0000the diffusion and nonlocal prey consumption in shaping the population\u0000distributions for interacting generalist predator and its focal prey\u0000species. In this regard, we first derive the conditions associated with\u0000Turing instability through linear analysis. Then, we perform a weakly\u0000nonlinear analysis and derive a cubic Stuart-Landau equation governing\u0000amplitude of the resulting patterns near Turing bifurcation boundary.\u0000Further, we present a wide variety of numerical simulations to\u0000corroborate our analytical findings as well as to illustrate some other\u0000complex spatiotemporal dynamics. Interestingly, our study reveals the\u0000existence of traveling wave solutions connecting two spatially\u0000homogeneous coexistence steady states in Turing domain under the\u0000influence of temporal bistability phenomenon. Also, our investigation\u0000shows that nonlocal prey consumption acts as a stabilizing force for the\u0000system dynamics.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2021-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41308462","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}
We address the problem of numerical simulation of suspensions of rigid particles in a Stokes flow. We focus on the inclusion of the singular short range interaction effects (lubrication effects) in the simulations when the particles come close one to another. The problem is solved without introducing new hypothesis nor model. As in Lefebvre-Lepot et al. [J. Fluid Mech. 769 (2015) 369–386], the key idea is to decompose the velocity and pressure flows in a sum of a singular and a regular part. In this article, the singular part is computed using an explicit asymptotic expansion of the solution when the distance goes to zero. This expansion is similar to the asymptotic expansion proposed in Hillairet and Kelai [Asymptotic Anal. 95 (2015) 187–241] but is more appropriate for numerical simulations of suspensions. It can be computed for any locally convex (that is the particles have to be convex close to the contact point) and regular shape of particles. Using Hillairet and Kelai [Asymptotic Anal. 95 (2015) 187–241] as an intermediate result, we prove that the remaining part is regular in the sense that it is bounded independently of the distance. As a consequence, only a small number of degrees of freedom are necessary to obtain accurate results. The method is tested in dimension 2 for clusters of two or three aligned particles with general rigid velocities. We show that, as expected, the convergence is independent of the distance.
研究了斯托克斯流中刚性颗粒悬浮液的数值模拟问题。我们重点研究了当粒子彼此靠近时的奇异短程相互作用效应(润滑效应)在模拟中的包含。这个问题不需要引入新的假设和模型就能解决。如Lefebvre-Lepot et al. [J]。流体力学[j] . 769(2015) 369-386]，关键思想是将速度和压力流动分解为奇异部分和正则部分之和。在本文中，奇异部分是用距离趋近于零时解的显式渐近展开来计算的。这种展开式类似于Hillairet和Kelai提出的渐近展开式[asymptotic Anal. 95(2015) 187-241]，但更适合于悬架的数值模拟。它可以计算任何局部凸(即粒子必须是靠近接触点的凸)和规则形状的粒子。使用Hillairet和Kelai[渐近分析，95(2015)187-241]作为中间结果，我们证明了剩余部分是正则的，因为它独立于距离有界。因此，只需要少量的自由度就可以获得准确的结果。该方法在二维中测试了具有一般刚性速度的两个或三个排列的粒子簇。我们证明，正如预期的那样，收敛性与距离无关。
{"title":"Numerical simulation of rigid particles in Stokes flow: lubrication correction for general shapes of particles","authors":"A. Lefebvre-Lepot, Flore Nabet","doi":"10.1051/MMNP/2021037","DOIUrl":"https://doi.org/10.1051/MMNP/2021037","url":null,"abstract":"We address the problem of numerical simulation of suspensions of rigid particles in a Stokes flow. We focus on the inclusion of the singular short range interaction effects (lubrication effects) in the simulations when the particles come close one to another. The problem is solved without introducing new hypothesis nor model. As in Lefebvre-Lepot et al. [J. Fluid Mech. 769 (2015) 369–386], the key idea is to decompose the velocity and pressure flows in a sum of a singular and a regular part. In this article, the singular part is computed using an explicit asymptotic expansion of the solution when the distance goes to zero. This expansion is similar to the asymptotic expansion proposed in Hillairet and Kelai [Asymptotic Anal. 95 (2015) 187–241] but is more appropriate for numerical simulations of suspensions. It can be computed for any locally convex (that is the particles have to be convex close to the contact point) and regular shape of particles. Using Hillairet and Kelai [Asymptotic Anal. 95 (2015) 187–241] as an intermediate result, we prove that the remaining part is regular in the sense that it is bounded independently of the distance. As a consequence, only a small number of degrees of freedom are necessary to obtain accurate results. The method is tested in dimension 2 for clusters of two or three aligned particles with general rigid velocities. We show that, as expected, the convergence is independent of the distance.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2021-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43714941","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}
In loop reactors the system is composed of several reactor units that are organized in a loop and the feeding takes place at one of several ports with switching of the feed port. In its simplest operation a pulse is formed and rotates around it, producing high temperatures which enable combustion of dilute streams. A limiting model with infinite number of units was derived. Rotating pulses, steady in a moving coordinate, emerge in both models when the switching to front propagation velocities ~1. But this behavior exists over a narrow domain. Simulations were conducted with generic first order Arrhenius kinetics. Experimental observations are reviewed. Outside the narrow frozen rotating pattern domain the system may exhibit multi- or quasi-periodic operation separated by domains of inactive reaction. The bifurcation set incorporates many 'finger'-like domains of complex frequency-locked solutions that allow to extend the operation domain with higher feed temperatures. Control is necessary to attain stable simple rotating frozen pattern within the narrow domains of active operation. Various tested control approaches are reviewed. Actual implementation of combustion in LR will involve several reactants of different ignition temperatures. Design and control should be aimed at producing locked fronts and avoid extinction of slower reactions.
{"title":"Dynamics and control of loop reactors - a review","authors":"M. Sheintuch, O. Nekhamkina","doi":"10.1051/MMNP/2021035","DOIUrl":"https://doi.org/10.1051/MMNP/2021035","url":null,"abstract":"In loop reactors the system is composed of several reactor units that are organized in a loop and the feeding takes place at one of several ports with switching of the feed port. In its simplest operation a pulse is formed and rotates around it, producing high temperatures which enable combustion of dilute streams. A limiting model with infinite number of units was derived. Rotating pulses, steady in a moving coordinate, emerge in both models when the switching to front propagation velocities ~1. But this behavior exists over a narrow domain. Simulations were conducted with generic first order Arrhenius kinetics. Experimental observations are reviewed.\u0000Outside the narrow frozen rotating pattern domain the system may exhibit multi- or quasi-periodic operation separated by domains of inactive reaction. The bifurcation set incorporates many 'finger'-like domains of complex frequency-locked solutions that allow to extend the operation domain with higher feed temperatures.\u0000Control is necessary to attain stable simple rotating frozen pattern within the narrow domains of active operation. Various tested control approaches are reviewed.\u0000 Actual implementation of combustion in LR will involve several reactants of different ignition temperatures. Design and control should be aimed at producing locked fronts and avoid extinction of slower reactions.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2021-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46721160","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}
We develop a method that completely characterizes the global dynamics of models with multiple subpopulations that are weakly interconnected. The method is applied on two classes of models with multiple subpopulations: an epidemic model that involves multiple host species and multiple vector species and a patchy vector-borne model. The method consists of two main steps: reducing the system using tools of large scale systems and studying the dynamics of an auxiliary system related the original system. The developed method determines the underlying dynamics and the ``weight" of each subpopulations with respect to the dynamics of the whole population, and how the topology of the connectivity matrix alters the dynamics of the overall population. The method provides global stability results for all types of equilibria, namely trivial, boundary or interior equilibria.
{"title":"Effects of Heterogeneity and Global Dynamics of Weakly Connected Subpopulations","authors":"Derdei Bichara, A. Iggidr, Souâd Yacheur","doi":"10.1051/MMNP/2021034","DOIUrl":"https://doi.org/10.1051/MMNP/2021034","url":null,"abstract":"We develop a method that completely characterizes the global dynamics of models with multiple subpopulations that are weakly interconnected. The method is applied on two classes of models with multiple subpopulations: an epidemic model that involves multiple host species and multiple vector species and a patchy vector-borne model. The method consists of two main steps: reducing the system using tools of large scale systems and studying the dynamics of an auxiliary system related the original system. The developed method determines the underlying dynamics and the ``weight\" of each subpopulations with respect to the dynamics of the whole population, and how the topology of the connectivity matrix alters the dynamics of the overall population. The method provides global stability results for all types of equilibria, namely trivial, boundary or interior equilibria.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2021-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46951992","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}
The interface dynamics of a 3D cell immersed in a 3D extracellular matrix is investigated. We suggest a 3D generalization of a known 2D minimal phase field model suggested in Ziebert et al. [J. R. Soc. Interface 9 (2012) 1084–1092] for the description of keratocyte motility. Our model consists of two coupled evolution equations for the order parameter and a three-dimensional vector field describing the actin network polarization (orientation). We derive a closed evolutionary integro-differential equation governing the interface dynamics of a 3D cell. The equation includes the normal velocity of the membrane, its curvature, cell volume relaxation, and a parameter that is determined by the non-equilibrium effects in the cytoskeleton. This equation can be considered as a 3D generalization of the 2D case that was studied in Abu Hamed and Nepomnyashchy [Physica D 408 (2020)].
研究了浸泡在三维细胞外基质中的三维细胞的界面动力学。我们建议对Ziebert等人[J.R.Soc.Interface 9（2012）1084-1092]中提出的已知2D最小相场模型进行3D推广，以描述角膜细胞运动。我们的模型由两个阶参数的耦合进化方程和一个描述肌动蛋白网络极化（取向）的三维矢量场组成。我们导出了一个控制三维细胞界面动力学的闭合进化积分微分方程。该方程包括膜的法向速度、曲率、细胞体积弛豫，以及由细胞骨架中的非平衡效应决定的参数。该方程可以被认为是Abu Hamed和Nepomnyashchy[Physica D 408（2020）]中研究的2D情况的3D推广。
{"title":"Three-dimensional phase field model for actin-based cell membrane dynamics","authors":"M. Hamed, A. Nepomnyashchy","doi":"10.1051/mmnp/2021048","DOIUrl":"https://doi.org/10.1051/mmnp/2021048","url":null,"abstract":"The interface dynamics of a 3D cell immersed in a 3D extracellular matrix is investigated. We suggest a 3D generalization of a known 2D minimal phase field model suggested in Ziebert et al. [J. R. Soc. Interface 9 (2012) 1084–1092] for the description of keratocyte motility. Our model consists of two coupled evolution equations for the order parameter and a three-dimensional vector field describing the actin network polarization (orientation). We derive a closed evolutionary integro-differential equation governing the interface dynamics of a 3D cell. The equation includes the normal velocity of the membrane, its curvature, cell volume relaxation, and a parameter that is determined by the non-equilibrium effects in the cytoskeleton. This equation can be considered as a 3D generalization of the 2D case that was studied in Abu Hamed and Nepomnyashchy [Physica D 408 (2020)].","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2021-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47229551","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}
karim O. Amin, Irina Badralexi, A. Halanay, R. Mghames
In this paper the stability of the zero equilibrium of a system with time delay is studied. The critical case of a multiple zero root of the characteristic equation of the linearized system is treated by applying a Malkin type theorem and using a complete Lyapunov-Krasovskii functional. An application to a model for malaria under treatment considering the action of the immune system is presented.
{"title":"A stability theorem for equilibria of delay differential equations in a critical case with application to a model of cell evolution","authors":"karim O. Amin, Irina Badralexi, A. Halanay, R. Mghames","doi":"10.1051/MMNP/2021021","DOIUrl":"https://doi.org/10.1051/MMNP/2021021","url":null,"abstract":"In this paper the stability of the zero equilibrium of a system with time delay is studied. The critical case of a multiple zero root of the characteristic equation of the linearized system is treated by applying a Malkin type theorem and using a complete Lyapunov-Krasovskii functional. An application to a model for malaria under treatment considering the action of the immune system is presented.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2021-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42817527","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}
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