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Discrete Leslie's model with bifurcations and control 离散莱斯利的分岔和控制模型
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231146
A. Khan, Ibraheem M. Alsulami
{"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}
引用次数: 0
Dynamical complexities and chaos control in a Ricker type predator-prey model with additive Allee effect 具有加性Allee效应的Ricker型捕食-食饵模型的动态复杂性和混沌控制
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231165
Vinoth Seralan, R. Vadivel, D. Chalishajar, N. Gunasekaran
{"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}
引用次数: 1
A novel approach for zero-inflated count regression model: Zero-inflated Poisson generalized-Lindley linear model with applications 零膨胀计数回归模型的一种新方法:零膨胀Poisson广义- lindley线性模型及其应用
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231183
E. Altun, Hana Alqifari, M. Eliwa
{"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}
引用次数: 0
Further representations and computations of the generalized Moore-Penrose inverse 广义Moore-Penrose逆的进一步表示和计算
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231191
Kezheng Zuo, Yang Chen, Li Yuan
{"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}
引用次数: 0
Riccati equation and metric geometric means of positive semidefinite matrices involving semi-tensor products 涉及半张量积的正半定矩阵的Riccati方程和度量几何均值
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231195
P. Chansangiam, Arnon Ploymukda
{"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}
引用次数: 1
A new subclass of analytic and bi-univalent functions associated with Legendre polynomials 与勒让德多项式相关的解析函数和双一元函数的一个新子类
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231196
Abeer O. Badghaish, Abdel Moneim Y. Lashin, Amani Z. Bajamal, Fayzah A. Alshehri
{"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}
引用次数: 2
Fixed-point results via $ alpha_{i}^{j} $-$ left({bf D}_{{mathscr{C}}}left(mathfrak{P}_{hat E}right)right) $-contractions in partial $ flat $-metric spaces 不动点结果通过$ alpha_{i}^{j} $ - $ left({bf D}_{{mathscr{C}}}left(mathfrak{P}_{hat E}right)right) $ -缩在部分$ flat $ -度量空间
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231204
Leyla Sağ Dönmez, Abdurrahman Büyükkaya, M. Öztürk
{"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}
引用次数: 0
A new error bound for linear complementarity problems involving $ B- $matrices 涉及$ B- $矩阵的线性互补问题的一个新的误差界
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231218
Hongmin Mo, Yingxue Dong
{"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}
引用次数: 0
Continuous Tsallis and Renyi extropy with pharmaceutical market application 连续的沙利和仁义外倾与医药市场应用
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231233
M. Mohamed, Najwan Alsadat, O. S. Balogun
{"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}
引用次数: 1
Unreliable retrial queueing system with working vacation 带工作假期的不可靠重审排队系统
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231234
Bharathy Shanmugam, M. C. Saravanarajan
{"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}
引用次数: 0
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