The objective of the current paper is to investigate the dynamics of a new predator–prey model, where the prey species obeys the law of logistic growth and is subjected to a non-smooth switched harvest: when the density of the prey is below a switched value, the harvest has a linear rate. Otherwise, the harvesting rate is constant. The equilibria of the proposed system are described, and the boundedness of its solutions is examined. We discuss the existence of periodic solutions; we show the appearance of two limit cycles, an unstable inner limit cycle and a stable outer one. As the values of the model parameters vary, several kinds of bifurcation for the model are detected, such as transcritical, saddle–node, and Hopf bifurcations. Finally, some numerical examples of the model are performed to confirm the theoretical results obtained.
{"title":"Dynamical behavior of predator–prey model with non-smooth prey harvesting","authors":"T. Meziani, N. Mohdeb","doi":"10.23939/mmc2023.02.261","DOIUrl":"https://doi.org/10.23939/mmc2023.02.261","url":null,"abstract":"The objective of the current paper is to investigate the dynamics of a new predator–prey model, where the prey species obeys the law of logistic growth and is subjected to a non-smooth switched harvest: when the density of the prey is below a switched value, the harvest has a linear rate. Otherwise, the harvesting rate is constant. The equilibria of the proposed system are described, and the boundedness of its solutions is examined. We discuss the existence of periodic solutions; we show the appearance of two limit cycles, an unstable inner limit cycle and a stable outer one. As the values of the model parameters vary, several kinds of bifurcation for the model are detected, such as transcritical, saddle–node, and Hopf bifurcations. Finally, some numerical examples of the model are performed to confirm the theoretical results obtained.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135585297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this work, we propose a mathematical model for describing the change in the ion density of the near-surface ionic layers of a semi-infinite metal. Through averaging over the subsystem of conduction electrons, we obtain in the adiabatic approximation an effective Hamiltonian of the ionic subsystem of a semi-infinite metal, which models the effect of the "metal–vacuum" separation surface on the structure of the near-surface ionic layers. We calculate the free energy of such a model and, by its minimization, obtain an equation for finding the displacements ξm of the ionic layer m. We show that in the absence of an inhomogeneous distribution of the electronic subsystem ξm≡0.
{"title":"Mathematical modeling of changes in density of near-surface ionic layers in semi-infinite metals. Equations for displacements of ionic layers","authors":"P. P. Kostrobij, B. M. Markovych, I. A. Ryzha","doi":"10.23939/mmc2023.03.988","DOIUrl":"https://doi.org/10.23939/mmc2023.03.988","url":null,"abstract":"In this work, we propose a mathematical model for describing the change in the ion density of the near-surface ionic layers of a semi-infinite metal. Through averaging over the subsystem of conduction electrons, we obtain in the adiabatic approximation an effective Hamiltonian of the ionic subsystem of a semi-infinite metal, which models the effect of the \"metal–vacuum\" separation surface on the structure of the near-surface ionic layers. We calculate the free energy of such a model and, by its minimization, obtain an equation for finding the displacements ξm of the ionic layer m. We show that in the absence of an inhomogeneous distribution of the electronic subsystem ξm≡0.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135798400","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Discriminant analysis is part of statistical learning; its goal is to separate classes defined a priori on a population and involves predicting the class of given data points. Discriminant analysis is applied in various fields such as pattern recognition, DNA microarray etc. In recent years, the discrimination problem remains a challenging task that has received increasing attention, especially for high-dimensional data sets. Indeed, in such a case, the feature selection is necessary, which implies the use of criteria of relevance, redundancy and complementarity of explanatory variables. The aim of this paper is to present an analysis of three new criteria proposed in this sense, more precisely based on the Principal Component Analysis we have been able to achieve a double objective: that of studying the harmony of these three criteria and also visualizing the class of candidate variables for a more in-depth selection in addition to eliminating the noise variables in a discriminant model.
{"title":"Statistical analysis of three new measures of relevance redundancy and complementarity","authors":"Hasna Chamlal, B. El Mourtji, T. Ouaderhman","doi":"10.23939/mmc2023.03.651","DOIUrl":"https://doi.org/10.23939/mmc2023.03.651","url":null,"abstract":"Discriminant analysis is part of statistical learning; its goal is to separate classes defined a priori on a population and involves predicting the class of given data points. Discriminant analysis is applied in various fields such as pattern recognition, DNA microarray etc. In recent years, the discrimination problem remains a challenging task that has received increasing attention, especially for high-dimensional data sets. Indeed, in such a case, the feature selection is necessary, which implies the use of criteria of relevance, redundancy and complementarity of explanatory variables. The aim of this paper is to present an analysis of three new criteria proposed in this sense, more precisely based on the Principal Component Analysis we have been able to achieve a double objective: that of studying the harmony of these three criteria and also visualizing the class of candidate variables for a more in-depth selection in addition to eliminating the noise variables in a discriminant model.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68768895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we propose a new mathematical model for joint Blind Deconvolution and Inpainting. The main objective is the treatment of blurred images with missing parts, through the game theory framework, in particular, a Nash game, we define two players: Player 1 handles the image intensity while Player 2, operates on the blur kernel. The two engage in a game until the equilibrium is reached. Finally, we provide some numerical examples: we compare the efficiency of our proposed approach to other existing methods in the literature that deals with Blind Deconvolution and Inpainting separately.
{"title":"A game theory approach for joint blind deconvolution and inpainting","authors":"N. Nasr, N. Moussaid, O. Gouasnouane","doi":"10.23939/mmc2023.03.674","DOIUrl":"https://doi.org/10.23939/mmc2023.03.674","url":null,"abstract":"In this paper we propose a new mathematical model for joint Blind Deconvolution and Inpainting. The main objective is the treatment of blurred images with missing parts, through the game theory framework, in particular, a Nash game, we define two players: Player 1 handles the image intensity while Player 2, operates on the blur kernel. The two engage in a game until the equilibrium is reached. Finally, we provide some numerical examples: we compare the efficiency of our proposed approach to other existing methods in the literature that deals with Blind Deconvolution and Inpainting separately.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68768930","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Many estimation methods have been proposed for the parameters of the regression models with serially correlated errors. In this work, we develop an asymptotic theory for estimation in the short panel data models with bilinear error. We propose a comparative study by simulation between several estimators (adaptive, ordinary and weighted least squares) for the coefficients of panel data models when the errors are bilinear serially correlated. As a consequence of the uniform local asymptotic normality property, we obtain adaptive estimates of the parameters. Finally, we illustrate the performance of the proposed estimators via Monte Carlo simulation study. We show that the adaptive estimates are more efficient than the weighted and ordinary least squares estimates.
{"title":"Estimation in short-panel data models with bilinear errors","authors":"A. Lmakri, A. Akharif, A. Mellouk","doi":"10.23939/mmc2023.03.682","DOIUrl":"https://doi.org/10.23939/mmc2023.03.682","url":null,"abstract":"Many estimation methods have been proposed for the parameters of the regression models with serially correlated errors. In this work, we develop an asymptotic theory for estimation in the short panel data models with bilinear error. We propose a comparative study by simulation between several estimators (adaptive, ordinary and weighted least squares) for the coefficients of panel data models when the errors are bilinear serially correlated. As a consequence of the uniform local asymptotic normality property, we obtain adaptive estimates of the parameters. Finally, we illustrate the performance of the proposed estimators via Monte Carlo simulation study. We show that the adaptive estimates are more efficient than the weighted and ordinary least squares estimates.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68768939","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Gene expression datasets have been successfully applied for a variety of purposes, including cancer classification. The challenges faced in developing effective classifiers for expression datasets are high dimensionality and over-fitting. Gene selection is an effective and efficient method to overcome these challenges and improve the predictive accuracy of a classifier. Based on PROMETHEE, this paper introduces a multi-filter ensemble approach by integrating the results of two potential filters namely MaCΨ-filter and PCRWG-filter to pre-select the most informative genes. Experiments were conducted on nine microarray datasets to demonstrate the performance of the proposed method.
{"title":"PROMETHEE filter-based method for microarray gene expression data","authors":"T. Ouaderhman, F. Aaboub, Hasna Chamlal","doi":"10.23939/mmc2023.03.693","DOIUrl":"https://doi.org/10.23939/mmc2023.03.693","url":null,"abstract":"Gene expression datasets have been successfully applied for a variety of purposes, including cancer classification. The challenges faced in developing effective classifiers for expression datasets are high dimensionality and over-fitting. Gene selection is an effective and efficient method to overcome these challenges and improve the predictive accuracy of a classifier. Based on PROMETHEE, this paper introduces a multi-filter ensemble approach by integrating the results of two potential filters namely MaCΨ-filter and PCRWG-filter to pre-select the most informative genes. Experiments were conducted on nine microarray datasets to demonstrate the performance of the proposed method.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68768949","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
K. El Hadadi, S. Elmoumen, S. Benzekri, O. Idrissi
In this paper, we will try to manage arrivals in the approach area of Mohammed V airport by solving two proposed algorithms "Scheduling with speeds limitations" and "Scheduling with speeds corrections", with a modified Bat algorithm, this modification involved the speed equation as well as the frequency equation of the standard Bat algorithm to avoid the phenomenon of slow convergence to the best solution in the search space of this algorithm. These proposed algorithms will allow us to schedule traffic optimally and to increase the capacity of the airport and better manage the controlled space approach area of Mohammed V Airport.
{"title":"Air traffic modeling and optimization by solving two new models with a modified algorithm","authors":"K. El Hadadi, S. Elmoumen, S. Benzekri, O. Idrissi","doi":"10.23939/mmc2023.03.712","DOIUrl":"https://doi.org/10.23939/mmc2023.03.712","url":null,"abstract":"In this paper, we will try to manage arrivals in the approach area of Mohammed V airport by solving two proposed algorithms \"Scheduling with speeds limitations\" and \"Scheduling with speeds corrections\", with a modified Bat algorithm, this modification involved the speed equation as well as the frequency equation of the standard Bat algorithm to avoid the phenomenon of slow convergence to the best solution in the search space of this algorithm. These proposed algorithms will allow us to schedule traffic optimally and to increase the capacity of the airport and better manage the controlled space approach area of Mohammed V Airport.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68769008","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The evolution scheme phase, in which the genetic algorithms select individuals that will form the new population, had an important impact on these algorithms. Many approaches exist in the literature. However, these approaches consider only the value of the fitness function to differenciate best solutions from the worst ones. This article introduces the parenting fitness, a novel parameter, that defines the capacity of an individual to produce fittest offsprings. Combining the standard fitness function and the parenting fitness helps the genetic algorithm to be more efficient, hence, producing best results.
{"title":"Genetic algorithm parenting fitness","authors":"M. Ouiss, A. Ettaoufik, A. Marzak, A. Tragha","doi":"10.23939/mmc2023.02.566","DOIUrl":"https://doi.org/10.23939/mmc2023.02.566","url":null,"abstract":"The evolution scheme phase, in which the genetic algorithms select individuals that will form the new population, had an important impact on these algorithms. Many approaches exist in the literature. However, these approaches consider only the value of the fitness function to differenciate best solutions from the worst ones. This article introduces the parenting fitness, a novel parameter, that defines the capacity of an individual to produce fittest offsprings. Combining the standard fitness function and the parenting fitness helps the genetic algorithm to be more efficient, hence, producing best results.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68769172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
On the example of the plane model of wheeled vehicle oscillations with adaptive power characteristic of the suspension system, the methodology for selecting its main parameters that would maximize the movement smoothness is developed. To solve this problem, the mathematical model of relative oscillations of the sprung part is constructed, provided that they are carried out in the vertical plane. The latter represents the system of two nonlinear differential equations describing the relative displacement of the center of mass of the sprung part and the angle of rotation of the latter around the transverse axis passing through the center of mass of the specified part. To construct the approximate analytical solution of this equations system, and thus to describe the main parameters that determine the relative position of the sprung part under reasonable assumptions, the method of normal oscillations of nonlinear systems with concentrated masses is used. This made it possible to obtain the system of ordinary differential equations of the first order that describe the amplitude–frequency characteristics of the sprung part vibrations. Due to the analysis of the latter it is determined that at a certain ratio between the parameters describing the power characteristics of the suspension system, it can perform isochronous vertical and longitudinal–angular oscillations, and thus it is possible to achieve maximum comfort in transporting passengers or dangerous cargo over rough terrain. The main obtained results can be used to create the software product for adaptive suspension, and their validity is confirmed by: a) in passing to the limit, obtaining results known from literary sources; b) generalization, based on the use of periodic Ateb-functions, of widely tested analytical methods for constructing solutions of differential equations with strong nonlinearity.
{"title":"Method of normal oscillations and substantiation of the choice of parameters for certain nonlinear systems with two degrees of freedom","authors":"B. Sokil, A. Senyk, M. Sokil, A. Y. Lisnichuk","doi":"10.23939/mmc2023.03.927","DOIUrl":"https://doi.org/10.23939/mmc2023.03.927","url":null,"abstract":"On the example of the plane model of wheeled vehicle oscillations with adaptive power characteristic of the suspension system, the methodology for selecting its main parameters that would maximize the movement smoothness is developed. To solve this problem, the mathematical model of relative oscillations of the sprung part is constructed, provided that they are carried out in the vertical plane. The latter represents the system of two nonlinear differential equations describing the relative displacement of the center of mass of the sprung part and the angle of rotation of the latter around the transverse axis passing through the center of mass of the specified part. To construct the approximate analytical solution of this equations system, and thus to describe the main parameters that determine the relative position of the sprung part under reasonable assumptions, the method of normal oscillations of nonlinear systems with concentrated masses is used. This made it possible to obtain the system of ordinary differential equations of the first order that describe the amplitude–frequency characteristics of the sprung part vibrations. Due to the analysis of the latter it is determined that at a certain ratio between the parameters describing the power characteristics of the suspension system, it can perform isochronous vertical and longitudinal–angular oscillations, and thus it is possible to achieve maximum comfort in transporting passengers or dangerous cargo over rough terrain. The main obtained results can be used to create the software product for adaptive suspension, and their validity is confirmed by: a) in passing to the limit, obtaining results known from literary sources; b) generalization, based on the use of periodic Ateb-functions, of widely tested analytical methods for constructing solutions of differential equations with strong nonlinearity.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68769596","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
El Youssoufi El Youssoufi, A. Kouidere, D. Kada, O. Balatif, A. Daouia, M. Rachik
In this work, we analyze a viral hepatitis C model. This epidemic remains a major problem for global public health, in all communities, despite the efforts made. The model is analyzed using the stability theory of systems of nonlinear differential equations. Based on the results of the analysis, the proposed model has two equilibrium points: a disease-free equilibrium point E0 and an endemic equilibrium point E∗. We investigate the existence of equilibrium point of the model. Furthermore, based on the indirect Lyapunov method, we study the local stability of each equilibrium point of the model. Moreover, by constructing the appropriate Lyapunov function and by using LaSalle invariance principle, we get some information on the global stability of equilibrium points under certain conditions. The basic reproduction number R0 is calculated using the Next Generation method. The positivity of the solutions and their bornitude have been proven, the existence of the solutions has also been proven. Optimal control of the system was studied by proposing three types of intervention: awareness program, early detection, isolation and treatment. The maximum principle of Pontryagin was used to characterize the optimal controls found. Numerical simulations were carried out with a finite numerical difference diagram and using MATLAB to confirm acquired results.
{"title":"On stability analysis study and strategies for optimal control of a mathematical model of hepatitis HCV with the latent state","authors":"El Youssoufi El Youssoufi, A. Kouidere, D. Kada, O. Balatif, A. Daouia, M. Rachik","doi":"10.23939/mmc2023.01.101","DOIUrl":"https://doi.org/10.23939/mmc2023.01.101","url":null,"abstract":"In this work, we analyze a viral hepatitis C model. This epidemic remains a major problem for global public health, in all communities, despite the efforts made. The model is analyzed using the stability theory of systems of nonlinear differential equations. Based on the results of the analysis, the proposed model has two equilibrium points: a disease-free equilibrium point E0 and an endemic equilibrium point E∗. We investigate the existence of equilibrium point of the model. Furthermore, based on the indirect Lyapunov method, we study the local stability of each equilibrium point of the model. Moreover, by constructing the appropriate Lyapunov function and by using LaSalle invariance principle, we get some information on the global stability of equilibrium points under certain conditions. The basic reproduction number R0 is calculated using the Next Generation method. The positivity of the solutions and their bornitude have been proven, the existence of the solutions has also been proven. Optimal control of the system was studied by proposing three types of intervention: awareness program, early detection, isolation and treatment. The maximum principle of Pontryagin was used to characterize the optimal controls found. Numerical simulations were carried out with a finite numerical difference diagram and using MATLAB to confirm acquired results.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135534692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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