We explored a local stability analysis at fixed points, bifurcations, and a control in a discrete Leslie's prey-predator model in the interior of $ mathbb{R}_+^2 $. More specially, it is examined that for all parameters, Leslie's model has boundary and interior equilibria, and the local stability is studied by the linear stability theory at equilibrium. Additionally, the model does not undergo a flip bifurcation at the boundary fixed point, though a Neimark-Sacker bifurcation exists at the interior fixed point, and no other bifurcation exists at this point. Furthermore, the Neimark-Sacker bifurcation is controlled by a hybrid control strategy. Finally, numerical simulations that validate the obtained results are given.
{"title":"Discrete Leslie's model with bifurcations and control","authors":"A. Khan, Ibraheem M. Alsulami","doi":"10.3934/math.20231146","DOIUrl":"https://doi.org/10.3934/math.20231146","url":null,"abstract":"We explored a local stability analysis at fixed points, bifurcations, and a control in a discrete Leslie's prey-predator model in the interior of $ mathbb{R}_+^2 $. More specially, it is examined that for all parameters, Leslie's model has boundary and interior equilibria, and the local stability is studied by the linear stability theory at equilibrium. Additionally, the model does not undergo a flip bifurcation at the boundary fixed point, though a Neimark-Sacker bifurcation exists at the interior fixed point, and no other bifurcation exists at this point. Furthermore, the Neimark-Sacker bifurcation is controlled by a hybrid control strategy. Finally, numerical simulations that validate the obtained results are given.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70161818","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Vinoth Seralan, R. Vadivel, D. Chalishajar, N. Gunasekaran
This work investigates the dynamic complications of the Ricker type predator-prey model in the presence of the additive type Allee effect in the prey population. In the modeling of discrete-time models, Euler forward approximations and piecewise constant arguments are the most frequently used schemes. In Euler forward approximations, the model may undergo period-doubled orbits and invariant circle orbits, even while varying the step size. In this way, differential equations with piecewise constant arguments (Ricker-type models) are a better choice for the discretization of a continuous-time model because they do not involve any step size. First, the interaction between prey and predator in the form of the Holling-Ⅱ type is considered. The essential mathematical features are discussed in terms of local stability and the bifurcation phenomenon as well. Next, we apply the center manifold theorem and normal form theory to achieve the existence and directions of flip bifurcation and Neimark-Sacker bifurcation. Moreover, this paper demonstrates that the outbreak of chaos can stabilize in the considered model with a higher value of the Allee parameter. The existence of chaotic orbits is verified with the help of a one-parameter bifurcation diagram and the largest Lyapunov exponents, respectively. Furthermore, different control methods are applied to control the bifurcation and fluctuating phenomena, i.e., state feedback, the Ott-Grebogi-Yorke, and hybrid control methods. Finally, to ensure our analytical results, numerical simulations have been carried out using MATLAB software.
{"title":"Dynamical complexities and chaos control in a Ricker type predator-prey model with additive Allee effect","authors":"Vinoth Seralan, R. Vadivel, D. Chalishajar, N. Gunasekaran","doi":"10.3934/math.20231165","DOIUrl":"https://doi.org/10.3934/math.20231165","url":null,"abstract":"This work investigates the dynamic complications of the Ricker type predator-prey model in the presence of the additive type Allee effect in the prey population. In the modeling of discrete-time models, Euler forward approximations and piecewise constant arguments are the most frequently used schemes. In Euler forward approximations, the model may undergo period-doubled orbits and invariant circle orbits, even while varying the step size. In this way, differential equations with piecewise constant arguments (Ricker-type models) are a better choice for the discretization of a continuous-time model because they do not involve any step size. First, the interaction between prey and predator in the form of the Holling-Ⅱ type is considered. The essential mathematical features are discussed in terms of local stability and the bifurcation phenomenon as well. Next, we apply the center manifold theorem and normal form theory to achieve the existence and directions of flip bifurcation and Neimark-Sacker bifurcation. Moreover, this paper demonstrates that the outbreak of chaos can stabilize in the considered model with a higher value of the Allee parameter. The existence of chaotic orbits is verified with the help of a one-parameter bifurcation diagram and the largest Lyapunov exponents, respectively. Furthermore, different control methods are applied to control the bifurcation and fluctuating phenomena, i.e., state feedback, the Ott-Grebogi-Yorke, and hybrid control methods. Finally, to ensure our analytical results, numerical simulations have been carried out using MATLAB software.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70162390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Count regression models are important statistical tools to model the discrete dependent variable with known covariates. When the dependent variable exhibits over-dispersion and inflation at zero point, the zero-inflated negative-binomial regression model is used. The presented paper offers a new model as an alternative to the zero-inflated negative-binomial regression model. To do this, Poisson generalized-Lindley distribution is re-parametrized and its parameter estimation problem is discussed via maximum likelihood estimation method. The proposed model is called as zero-inflated Poisson generalized Lindley regression model. The results regarding the efficiency of parameter estimation of the proposed model are evaluated with two simulation studies. To evaluate the success of the proposed model in the case of zero inflation, two datasets are analyzed. According to the results obtained, the proposed model gives better results than the negative-binomial regression model both in case of over-dispersion and in the case of zero inflation.
{"title":"A novel approach for zero-inflated count regression model: Zero-inflated Poisson generalized-Lindley linear model with applications","authors":"E. Altun, Hana Alqifari, M. Eliwa","doi":"10.3934/math.20231183","DOIUrl":"https://doi.org/10.3934/math.20231183","url":null,"abstract":"Count regression models are important statistical tools to model the discrete dependent variable with known covariates. When the dependent variable exhibits over-dispersion and inflation at zero point, the zero-inflated negative-binomial regression model is used. The presented paper offers a new model as an alternative to the zero-inflated negative-binomial regression model. To do this, Poisson generalized-Lindley distribution is re-parametrized and its parameter estimation problem is discussed via maximum likelihood estimation method. The proposed model is called as zero-inflated Poisson generalized Lindley regression model. The results regarding the efficiency of parameter estimation of the proposed model are evaluated with two simulation studies. To evaluate the success of the proposed model in the case of zero inflation, two datasets are analyzed. According to the results obtained, the proposed model gives better results than the negative-binomial regression model both in case of over-dispersion and in the case of zero inflation.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70162905","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The aim of this paper is to provide new representations and computations of the generalized Moore-Penrose inverse. Based on the Moore-Penrose inverse, group inverse, Bott-Duffin inverse and certain projections, some representations for the generalized Moore-Penrose inverse are given. An equivalent condition for the continuity of the generalized Moore-Penrose inverse is proposed. Splitting methods and successive matrix squaring algorithm for computing the generalized Moore-Penrose inverse are presented.
{"title":"Further representations and computations of the generalized Moore-Penrose inverse","authors":"Kezheng Zuo, Yang Chen, Li Yuan","doi":"10.3934/math.20231191","DOIUrl":"https://doi.org/10.3934/math.20231191","url":null,"abstract":"The aim of this paper is to provide new representations and computations of the generalized Moore-Penrose inverse. Based on the Moore-Penrose inverse, group inverse, Bott-Duffin inverse and certain projections, some representations for the generalized Moore-Penrose inverse are given. An equivalent condition for the continuity of the generalized Moore-Penrose inverse is proposed. Splitting methods and successive matrix squaring algorithm for computing the generalized Moore-Penrose inverse are presented.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70162999","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We investigate the Riccati matrix equation $ X A^{-1} X = B $ in which the conventional matrix products are generalized to the semi-tensor products $ ltimes $. When $ A $ and $ B $ are positive definite matrices satisfying the factor-dimension condition, this equation has a unique positive definite solution, which is defined to be the metric geometric mean of $ A $ and $ B $. We show that this geometric mean is the maximum solution of the Riccati inequality. We then extend the notion of the metric geometric mean to positive semidefinite matrices by a continuity argument and investigate its algebraic properties, order properties and analytic properties. Moreover, we establish some equations and inequalities of metric geometric means for matrices involving cancellability, positive linear map and concavity. Our results generalize the conventional metric geometric means of matrices.
研究了Riccati矩阵方程$ X A^{-1} X = B $，其中常规矩阵积推广为半张量积$ ltimes $。当$ A $和$ B $为满足因子维条件的正定矩阵时，该方程有一个唯一的正定解，定义为$ A $和$ B $的度量几何平均值。我们证明了这个几何平均值是里卡蒂不等式的最大解。然后通过连续性论证将度量几何均值的概念推广到正半定矩阵，并研究了它的代数性质、阶性质和解析性质。此外，我们还建立了包含可消性、正线性映射和凹性的矩阵的度量几何均值的方程和不等式。我们的结果推广了矩阵的常规度量几何平均值。
{"title":"Riccati equation and metric geometric means of positive semidefinite matrices involving semi-tensor products","authors":"P. Chansangiam, Arnon Ploymukda","doi":"10.3934/math.20231195","DOIUrl":"https://doi.org/10.3934/math.20231195","url":null,"abstract":"We investigate the Riccati matrix equation $ X A^{-1} X = B $ in which the conventional matrix products are generalized to the semi-tensor products $ ltimes $. When $ A $ and $ B $ are positive definite matrices satisfying the factor-dimension condition, this equation has a unique positive definite solution, which is defined to be the metric geometric mean of $ A $ and $ B $. We show that this geometric mean is the maximum solution of the Riccati inequality. We then extend the notion of the metric geometric mean to positive semidefinite matrices by a continuity argument and investigate its algebraic properties, order properties and analytic properties. Moreover, we establish some equations and inequalities of metric geometric means for matrices involving cancellability, positive linear map and concavity. Our results generalize the conventional metric geometric means of matrices.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70163285","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abeer O. Badghaish, Abdel Moneim Y. Lashin, Amani Z. Bajamal, Fayzah A. Alshehri
In this paper, we introduce a new subclass of analytic and bi-univalent functions in the open unit disc $ U. $ For this subclass of functions, estimates of the initial coefficients $ leftvert A_{2}rightvert $ and $ leftvert A_{3}rightvert $ of the Taylor-Maclaurin series are given. An application of Legendre polynomials to this subclass of functions is presented. Furthermore, our study discusses several special cases.
{"title":"A new subclass of analytic and bi-univalent functions associated with Legendre polynomials","authors":"Abeer O. Badghaish, Abdel Moneim Y. Lashin, Amani Z. Bajamal, Fayzah A. Alshehri","doi":"10.3934/math.20231196","DOIUrl":"https://doi.org/10.3934/math.20231196","url":null,"abstract":"In this paper, we introduce a new subclass of analytic and bi-univalent functions in the open unit disc $ U. $ For this subclass of functions, estimates of the initial coefficients $ leftvert A_{2}rightvert $ and $ leftvert A_{3}rightvert $ of the Taylor-Maclaurin series are given. An application of Legendre polynomials to this subclass of functions is presented. Furthermore, our study discusses several special cases.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"42 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70163671","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Leyla Sağ Dönmez, Abdurrahman Büyükkaya, M. Öztürk
In this study, we characterize a novel contraction mapping referred to as $ alpha_{i}^{j} $-$ left({bf D}_{{mathscr{C}}}left(mathfrak{P}_{hat E}right)right) $-contraction in light of $ {bf D}_{mathscr{C}} $-contraction mappings associated with the Geraghty-type contraction and $ E $-type contraction. Besides, a novel common fixed-point theorem providing such mappings is demonstrated in the context of partial $ flat $-metric spaces. It is stated that the main theorem is a generalization of the existing literature, and its comparisons with the results are expressed. Additionally, the efficiency of the result of this study is demonstrated through some examples and an application to homotopy theory.
{"title":"Fixed-point results via $ alpha_{i}^{j} $-$ left({bf D}_{{mathscr{C}}}left(mathfrak{P}_{hat E}right)right) $-contractions in partial $ flat $-metric spaces","authors":"Leyla Sağ Dönmez, Abdurrahman Büyükkaya, M. Öztürk","doi":"10.3934/math.20231204","DOIUrl":"https://doi.org/10.3934/math.20231204","url":null,"abstract":"In this study, we characterize a novel contraction mapping referred to as $ alpha_{i}^{j} $-$ left({bf D}_{{mathscr{C}}}left(mathfrak{P}_{hat E}right)right) $-contraction in light of $ {bf D}_{mathscr{C}} $-contraction mappings associated with the Geraghty-type contraction and $ E $-type contraction. Besides, a novel common fixed-point theorem providing such mappings is demonstrated in the context of partial $ flat $-metric spaces. It is stated that the main theorem is a generalization of the existing literature, and its comparisons with the results are expressed. Additionally, the efficiency of the result of this study is demonstrated through some examples and an application to homotopy theory.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70163768","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, a new error bound for the linear complementarity problems of $ B- $matrices which is a subclass of the $ P- $matrices is presented. Theoretical analysis and numerical example illustrate that the new error bound improves some existing results.
{"title":"A new error bound for linear complementarity problems involving $ B- $matrices","authors":"Hongmin Mo, Yingxue Dong","doi":"10.3934/math.20231218","DOIUrl":"https://doi.org/10.3934/math.20231218","url":null,"abstract":"In this paper, a new error bound for the linear complementarity problems of $ B- $matrices which is a subclass of the $ P- $matrices is presented. Theoretical analysis and numerical example illustrate that the new error bound improves some existing results.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70164314","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, the Tsallis and Renyi extropy is presented as a continuous measure of information under the continuous distribution. Furthermore, the features and their connection to other information measures are introduced. Some stochastic comparisons and results on the order statistics and upper records are given. Moreover, some theorems about the maximum Tsallis and Renyi extropy are discussed. On the other hand, numerical results of the non-parametric estimation of Tsallis extropy are calculated for simulated and real data with application to time series model and its forecasting.
{"title":"Continuous Tsallis and Renyi extropy with pharmaceutical market application","authors":"M. Mohamed, Najwan Alsadat, O. S. Balogun","doi":"10.3934/math.20231233","DOIUrl":"https://doi.org/10.3934/math.20231233","url":null,"abstract":"In this paper, the Tsallis and Renyi extropy is presented as a continuous measure of information under the continuous distribution. Furthermore, the features and their connection to other information measures are introduced. Some stochastic comparisons and results on the order statistics and upper records are given. Moreover, some theorems about the maximum Tsallis and Renyi extropy are discussed. On the other hand, numerical results of the non-parametric estimation of Tsallis extropy are calculated for simulated and real data with application to time series model and its forecasting.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70164915","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper investigates an unreliable $ M/G(P_{1}, P_{2})/1 $ retrial queueing system with a woking vacation. An arriving customer successfully starts the first phase service with the probability $ alpha $ or the server fails with the probability $ bar{alpha} $. Once failure happens, the serving customer is taken to the orbit. The failed server is taken for repair with some delay. Once the repair is comleted, the server is ready to provide service once again. In this background, we implemented the working vacation scenario. During working vacation, the service will be provided at a slower rate, rather than entirely stopping the service. The supplementary variable method was adopted to find the orbit and system lengths. Additionally, some unique results and numerical evaluations have been presented.
{"title":"Unreliable retrial queueing system with working vacation","authors":"Bharathy Shanmugam, M. C. Saravanarajan","doi":"10.3934/math.20231234","DOIUrl":"https://doi.org/10.3934/math.20231234","url":null,"abstract":"This paper investigates an unreliable $ M/G(P_{1}, P_{2})/1 $ retrial queueing system with a woking vacation. An arriving customer successfully starts the first phase service with the probability $ alpha $ or the server fails with the probability $ bar{alpha} $. Once failure happens, the serving customer is taken to the orbit. The failed server is taken for repair with some delay. Once the repair is comleted, the server is ready to provide service once again. In this background, we implemented the working vacation scenario. During working vacation, the service will be provided at a slower rate, rather than entirely stopping the service. The supplementary variable method was adopted to find the orbit and system lengths. Additionally, some unique results and numerical evaluations have been presented.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70165316","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：