S. Jesic, N. Ćirović, R. Nikolić, Branislav M. Ranƌelović
The main motivation for this paper is to investigate the fixed point property for non-expansive mappings defined on $ b $-fuzzy metric spaces. First, following the idea of S. Ješić's result from 2009, we introduce convex, strictly convex and normal structures for sets in $ b $-fuzzy metric spaces. By using topological methods and these notions, we prove the existence of fixed points for self-mappings defined on $ b $-fuzzy metric spaces satisfying a nonlinear type condition. This result generalizes and improves many previously known results, such as W. Takahashi's result on metric spaces from 1970. A representative example illustrating the main result is provided.
本文的主要动机是研究定义在$ b $-模糊度量空间上的非扩展映射的不动点性质。首先，根据s. Ješić在2009年的结果，我们引入了$ b $-模糊度量空间集合的凸结构、严格凸结构和正规结构。利用拓扑方法和这些概念，证明了在满足非线性型条件的$ b $-模糊度量空间上定义的自映射不动点的存在性。这个结果推广并改进了许多先前已知的结果，例如W. Takahashi在1970年关于度量空间的结果。给出了一个代表性的例子来说明主要结果。
{"title":"A fixed point theorem in strictly convex $ b $-fuzzy metric spaces","authors":"S. Jesic, N. Ćirović, R. Nikolić, Branislav M. Ranƌelović","doi":"10.3934/math.20231068","DOIUrl":"https://doi.org/10.3934/math.20231068","url":null,"abstract":"The main motivation for this paper is to investigate the fixed point property for non-expansive mappings defined on $ b $-fuzzy metric spaces. First, following the idea of S. Ješić's result from 2009, we introduce convex, strictly convex and normal structures for sets in $ b $-fuzzy metric spaces. By using topological methods and these notions, we prove the existence of fixed points for self-mappings defined on $ b $-fuzzy metric spaces satisfying a nonlinear type condition. This result generalizes and improves many previously known results, such as W. Takahashi's result on metric spaces from 1970. A representative example illustrating the main result is provided.","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":"70157647","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 goal of this paper is to create an algebraic structure based on single-valued neutrosophic sets. We present a novel approach to the neutrosophic sub-ring and ideal by combining the classical ring with neutrosophic sets. We also introduce and investigate some of the fundamental properties of the concepts. Finally, we show how to use a neutrosophic ideal to make a decision.
{"title":"Results on a neutrosophic sub-rings","authors":"Amr Elrawy, Mohamed A. M. Abdalla","doi":"10.3934/math.20231090","DOIUrl":"https://doi.org/10.3934/math.20231090","url":null,"abstract":"The goal of this paper is to create an algebraic structure based on single-valued neutrosophic sets. We present a novel approach to the neutrosophic sub-ring and ideal by combining the classical ring with neutrosophic sets. We also introduce and investigate some of the fundamental properties of the concepts. Finally, we show how to use a neutrosophic ideal to make a decision.","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":"70158467","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}
Fuzzy systems of equations often appear while modeling physical systems with imprecisely defined parameters. Many mathematical methods are available to investigate them, but handling them is challenging due to the computational complexity and difficult implementation. As such, in this paper, the Inner-Outer Direct Search (IODS) optimization technique is extended in the fuzzy environment to solve a fuzzy system of nonlinear equations. The main purpose of the extension is to study the system variables in the presence of fuzzy information. To manage fuzziness, a fuzzy parametric form is employed in the uncertain system and controls the search process toward the optimal solution. The proposed approach of fuzzy IODS converts the fuzzy system of nonlinear equations to an unconstrained fuzzy optimization problem. Then, the unconstrained fuzzy optimization problem is studied through the IODS technique. To solve the unconstrained fuzzy optimization problem, the fuzzy objective function is minimized with the help of exploratory and pattern search approaches. These searches are performed with inner and outer computations. Then, the obtained united solution provides the desired solution which minimizes the objective function. From the same the uncertain system, variables are derived. To verify the solution and proposed algorithm, convergence analysis is performed. Three case studies are considered with only fuzzy and fully fuzzy systems, and various cases are discussed. A comparison with other methods is made to test the efficacy of the method. The proposed algorithm is coded with the help of MATLAB software, and the results are analyzed graphically. Finally, the simple procedure and computationally efficient approach may help to implement the same in many engineering and science problems that can be modeled into systems of equations.
{"title":"Numerical investigation of non-probabilistic systems using Inner Outer Direct Search optimization technique","authors":"P. K. Panigrahi, S. Nayak","doi":"10.3934/math.20231087","DOIUrl":"https://doi.org/10.3934/math.20231087","url":null,"abstract":"Fuzzy systems of equations often appear while modeling physical systems with imprecisely defined parameters. Many mathematical methods are available to investigate them, but handling them is challenging due to the computational complexity and difficult implementation. As such, in this paper, the Inner-Outer Direct Search (IODS) optimization technique is extended in the fuzzy environment to solve a fuzzy system of nonlinear equations. The main purpose of the extension is to study the system variables in the presence of fuzzy information. To manage fuzziness, a fuzzy parametric form is employed in the uncertain system and controls the search process toward the optimal solution. The proposed approach of fuzzy IODS converts the fuzzy system of nonlinear equations to an unconstrained fuzzy optimization problem. Then, the unconstrained fuzzy optimization problem is studied through the IODS technique. To solve the unconstrained fuzzy optimization problem, the fuzzy objective function is minimized with the help of exploratory and pattern search approaches. These searches are performed with inner and outer computations. Then, the obtained united solution provides the desired solution which minimizes the objective function. From the same the uncertain system, variables are derived. To verify the solution and proposed algorithm, convergence analysis is performed. Three case studies are considered with only fuzzy and fully fuzzy systems, and various cases are discussed. A comparison with other methods is made to test the efficacy of the method. The proposed algorithm is coded with the help of MATLAB software, and the results are analyzed graphically. Finally, the simple procedure and computationally efficient approach may help to implement the same in many engineering and science problems that can be modeled into systems of equations.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"82 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70158760","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 purpose of this paper is to present a two-step approach for finding the series solution of the stochastic Newell-Whitehead-Segel (NWS) equation. The proposed two-step approach starts with the use of the Wiener-Hermite expansion (WHE) technique, which allows the conversion of the stochastic problem into a set of coupled deterministic partial differential equations (PDEs) by components. The deterministic kernels of the WHE serve as the solution to the stochastic NWS equation by decomposing the stochastic process. The second step involves solving these PDEs using the reduced differential transform (RDT) algorithm, which enables the determination of the deterministic kernels. The final step involves plugging these kernels back into the WHE to derive the series solution of the stochastic NWS equation. The expectation and variance of the solution are calculated and graphically displayed to provide a clear visual representation of the results. We believe that this two-step technique for computing the series solution process can be used to a great extent for stochastic PDEs arising in a variety of sciences.
{"title":"On the series solution of the stochastic Newell Whitehead Segel equation","authors":"J. Hussain","doi":"10.3934/math.20231100","DOIUrl":"https://doi.org/10.3934/math.20231100","url":null,"abstract":"The purpose of this paper is to present a two-step approach for finding the series solution of the stochastic Newell-Whitehead-Segel (NWS) equation. The proposed two-step approach starts with the use of the Wiener-Hermite expansion (WHE) technique, which allows the conversion of the stochastic problem into a set of coupled deterministic partial differential equations (PDEs) by components. The deterministic kernels of the WHE serve as the solution to the stochastic NWS equation by decomposing the stochastic process. The second step involves solving these PDEs using the reduced differential transform (RDT) algorithm, which enables the determination of the deterministic kernels. The final step involves plugging these kernels back into the WHE to derive the series solution of the stochastic NWS equation. The expectation and variance of the solution are calculated and graphically displayed to provide a clear visual representation of the results. We believe that this two-step technique for computing the series solution process can be used to a great extent for stochastic PDEs arising in a variety of sciences.","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":"70159237","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}
Constraint violation correction is an important research topic in solving multibody system dynamics. For a multibody system dynamics method which derives acceleration equations in a recursive manner and avoids overall dynamics equations, a fast and accurate solution to the violation problem is paramount. The direct correction method is favored due to its simplicity, high accuracy and low computational cost. This method directly supplements the constraint equations and performs corrections, making it an effective solution for addressing violation problems. However, calculating the significant Jacobian matrices for this method using dynamics equations can be challenging, especially for complex multibody systems. This paper presents a programmatic framework for deriving Jacobian matrices of planar rigid-flexible-multibody systems in a simple semi-analytic form along two paths separated by a secondary joint. The approach is verified by comparing constraint violation errors with and without the constraint violation correction in numerical examples. Moreover, the proposed method's computational speed is compared with that of the direct differential solution, verifying its efficiency. The straightforward, highly programmable and universal approach provides a new idea for programming large-scale dynamics software and extends the application of dynamics methods focused on deriving acceleration equations.
{"title":"A framework for establishing constraint Jacobian matrices of planar rigid-flexible-multibody systems","authors":"Lina Zhang, X. Rui, Jianshu Zhang, Guoping Wang, J. Gu, Xizhe Zhang","doi":"10.3934/math.20231096","DOIUrl":"https://doi.org/10.3934/math.20231096","url":null,"abstract":"Constraint violation correction is an important research topic in solving multibody system dynamics. For a multibody system dynamics method which derives acceleration equations in a recursive manner and avoids overall dynamics equations, a fast and accurate solution to the violation problem is paramount. The direct correction method is favored due to its simplicity, high accuracy and low computational cost. This method directly supplements the constraint equations and performs corrections, making it an effective solution for addressing violation problems. However, calculating the significant Jacobian matrices for this method using dynamics equations can be challenging, especially for complex multibody systems. This paper presents a programmatic framework for deriving Jacobian matrices of planar rigid-flexible-multibody systems in a simple semi-analytic form along two paths separated by a secondary joint. The approach is verified by comparing constraint violation errors with and without the constraint violation correction in numerical examples. Moreover, the proposed method's computational speed is compared with that of the direct differential solution, verifying its efficiency. The straightforward, highly programmable and universal approach provides a new idea for programming large-scale dynamics software and extends the application of dynamics methods focused on deriving acceleration equations.","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":"70159331","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 is concerned with piecewise pseudo almost periodic solutions of a class of interval general BAM neural networks with mixed time-varying delays and impulsive perturbations. By adopting the exponential dichotomy of linear differential equations and the fixed point theory of contraction mapping. The sufficient conditions for the existence of piecewise pseudo almost periodic solutions of the interval general BAM neural networks with mixed time-varying delays and impulsive perturbations are obtained. By adopting differential inequality techniques and mathematical methods of induction, the global exponential stability for the piecewise pseudo almost periodic solutions of the interval general BAM neural networks with mixed time-varying delays and impulsive perturbations is discussed. An example is given to illustrate the effectiveness of the results obtained in the paper.
{"title":"Piecewise pseudo almost periodic solutions of interval general BAM neural networks with mixed time-varying delays and impulsive perturbations","authors":"Yanshou Dong, Junfang Zhao, Xu Miao, Ming Kang","doi":"10.3934/math.20231113","DOIUrl":"https://doi.org/10.3934/math.20231113","url":null,"abstract":"This paper is concerned with piecewise pseudo almost periodic solutions of a class of interval general BAM neural networks with mixed time-varying delays and impulsive perturbations. By adopting the exponential dichotomy of linear differential equations and the fixed point theory of contraction mapping. The sufficient conditions for the existence of piecewise pseudo almost periodic solutions of the interval general BAM neural networks with mixed time-varying delays and impulsive perturbations are obtained. By adopting differential inequality techniques and mathematical methods of induction, the global exponential stability for the piecewise pseudo almost periodic solutions of the interval general BAM neural networks with mixed time-varying delays and impulsive perturbations is discussed. An example is given to illustrate the effectiveness of the results obtained in the paper.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"265 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70160109","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 concept of $ k $-folded $ mathcal{N} $-structures ($ k $-F$ mathcal{N} $Ss) is an essential concept to be considered for tackling intricate and tricky data. In this study, we want to broaden the notion of $ k $-F$ mathcal{N} $S by providing a general algebraic structure for tackling $ k $-folded $ mathcal{N} $-data by fusing the conception of semigroup and $ k $-F$ mathcal{N} $S. First, we introduce and study some algebraic properties of $ k $-F$ mathcal{N} $Ss, for instance, subset, characteristic function, union, intersection, complement and product of $ k $-F$ mathcal{N} $Ss, and support them by illustrative examples. We also propose $ k $-folded $ mathcal{N} $-subsemigroups ($ k $-F$ mathcal{N} $SBs) and $ widetilde{zeta} $-$ k $-folded $ mathcal{N} $-subsemigroups ($ widetilde{zeta} $-$ k $-F$ mathcal{N} $SBs) in the structure of semigroups and explore some attributes of these concepts. Characterizations of subsemigroups are considered based on these concepts. Using the notion of $ k $-folded $ mathcal{N} $-product, characterizations of $ k $-F$ mathcal{N} $SBs are also discussed. Further, we obtain a necessary condition of a $ k $-F$ mathcal{N} $SB to be a $ k $-folded $ mathcal{N} $-idempotent. Finally, relations between $ k $-folded $ mathcal{N} $-intersection and $ k $-folded $ mathcal{N} $-product are displayed, and how the image and inverse image of a $ k $-F$ mathcal{N} $SB become a $ k $-F$ mathcal{N} $SB is studied.
$ k $-fold $ mathcal{N} $-结构($ k $-F$ mathcal{N} $ s)的概念是处理复杂和棘手数据时需要考虑的基本概念。在本研究中，我们希望通过融合半群和$ k $-F$ mathcal{N} $S的概念，为处理$ k $-折叠$ mathcal{N} $-数据提供一个通用的代数结构，从而扩展$ k $-F$ mathcal{N} $S的概念。首先，介绍和研究了$ k $-F$ mathcal{N} $ s的子集、特征函数、并集、交、补和积等代数性质，并用实例进行了说明。我们还在半群结构中提出了$ k $-折叠$ mathcal{N} $-子半群($ k $-f $ mathcal{N} $SBs)和$ widdetilde {zeta} $-$ k $-折叠$ mathcal{N} $-子半群($ widdetilde {zeta} $-$ k $-f $ mathcal{N} $SBs)，并探讨了这些概念的一些属性。基于这些概念考虑子半群的特征。利用$ k $-折叠$ mathcal{N} $-积的概念，讨论了$ k $-F$ mathcal{N} $SBs的刻画。进一步，我们得到了$ k $-F$ mathcal{N} $SB是$ k $-折叠$ mathcal{N} $-幂等的必要条件。最后，给出了$ k $-折叠$ mathcal{N} $-交与$ k $-折叠$ mathcal{N} $-积之间的关系，并研究了$ k $-F$ mathcal{N} $SB的正反像如何变成$ k $-F$ mathcal{N} $SB。
{"title":"Operational algebraic properties and subsemigroups of semigroups in view of $ k $-folded $ mathcal{N} $-structures","authors":"Anas Al-Masarwah, Mohammed Alqahtani","doi":"10.3934/math.20231125","DOIUrl":"https://doi.org/10.3934/math.20231125","url":null,"abstract":"The concept of $ k $-folded $ mathcal{N} $-structures ($ k $-F$ mathcal{N} $Ss) is an essential concept to be considered for tackling intricate and tricky data. In this study, we want to broaden the notion of $ k $-F$ mathcal{N} $S by providing a general algebraic structure for tackling $ k $-folded $ mathcal{N} $-data by fusing the conception of semigroup and $ k $-F$ mathcal{N} $S. First, we introduce and study some algebraic properties of $ k $-F$ mathcal{N} $Ss, for instance, subset, characteristic function, union, intersection, complement and product of $ k $-F$ mathcal{N} $Ss, and support them by illustrative examples. We also propose $ k $-folded $ mathcal{N} $-subsemigroups ($ k $-F$ mathcal{N} $SBs) and $ widetilde{zeta} $-$ k $-folded $ mathcal{N} $-subsemigroups ($ widetilde{zeta} $-$ k $-F$ mathcal{N} $SBs) in the structure of semigroups and explore some attributes of these concepts. Characterizations of subsemigroups are considered based on these concepts. Using the notion of $ k $-folded $ mathcal{N} $-product, characterizations of $ k $-F$ mathcal{N} $SBs are also discussed. Further, we obtain a necessary condition of a $ k $-F$ mathcal{N} $SB to be a $ k $-folded $ mathcal{N} $-idempotent. Finally, relations between $ k $-folded $ mathcal{N} $-intersection and $ k $-folded $ mathcal{N} $-product are displayed, and how the image and inverse image of a $ k $-F$ mathcal{N} $SB become a $ k $-F$ mathcal{N} $SB is studied.","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":"70160690","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 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}
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