Pub Date : 2020-01-01DOI: 10.1007/978-3-030-36468-7_8
T. Lyche
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Pub Date : 2019-11-15DOI: 10.4236/alamt.2019.94007
Yafei Yang, Yuanfu Shao, Mengwei Li
In this paper, astochastic predator-prey systems with nonlinear harvesting and impulsive effect are investigated. Firstly, we show the existence and uniqueness of the global positive solution of the system. Secondly, by constructing appropriate Lyapunov function and using comparison theorem with an impulsive differential equation, we study that a positive periodic solution exists. Thirdly, we prove that system is globally attractive. Finally, numerical simulations are presented to show the feasibility of the obtained results.
{"title":"Periodic Solution for Stochastic Predator-Prey Systems with Nonlinear Harvesting and Impulses","authors":"Yafei Yang, Yuanfu Shao, Mengwei Li","doi":"10.4236/alamt.2019.94007","DOIUrl":"https://doi.org/10.4236/alamt.2019.94007","url":null,"abstract":"In this paper, astochastic predator-prey systems with nonlinear harvesting \u0000and impulsive effect are investigated. Firstly, we show the existence and uniqueness \u0000of the global positive solution of the system. Secondly, by constructing \u0000appropriate Lyapunov function and using comparison theorem with an \u0000impulsive differential equation, we study that a positive periodic solution exists. \u0000Thirdly, we prove that system is globally attractive. Finally, numerical \u0000simulations are presented to show the feasibility of the obtained results.","PeriodicalId":65610,"journal":{"name":"线性代数与矩阵理论研究进展(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76534963","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}
Pub Date : 2019-09-04DOI: 10.4236/alamt.2019.93004
Balasubramani Prema Rangasamy
To explore the various kind of matrices, matrix multiplication, identity matrix, characteristic equation, minimal polynomial and diagonalization, my paper investigates matrices and algebraic operations defined on them. These matrices may be viewed as rectangular array of elements where each entry depends on two subscripts. System of linear equations and their solutions may be efficiently investigated using the language of matrices. Furthermore, certain abstract objects introduced in the end of my papers, such as I-matrix, J-matrix, Transprocal of certain matrix, transpose of transprocal matrix, i.e. transprocose matrix, super orthogonality, super unitary, trans othogonaliity, and trans orthoprocal, can be represented by this matrix. On the other hand, the abstract treatment of linear algebra presented later will give us a new insight into the structure of these matrices. The entries in our matrices will come from some arbitrary, but fixed, field K.
{"title":"Matrices—One Review","authors":"Balasubramani Prema Rangasamy","doi":"10.4236/alamt.2019.93004","DOIUrl":"https://doi.org/10.4236/alamt.2019.93004","url":null,"abstract":"To explore the various kind of matrices, matrix multiplication, identity matrix, characteristic equation, minimal polynomial and diagonalization, my paper investigates matrices and algebraic operations defined on them. These matrices may be viewed as rectangular array of elements where each entry depends on two subscripts. System of linear equations and their solutions may be efficiently investigated using the language of matrices. Furthermore, certain abstract objects introduced in the end of my papers, such as I-matrix, J-matrix, Transprocal of certain matrix, transpose of transprocal matrix, i.e. transprocose matrix, super orthogonality, super unitary, trans othogonaliity, and trans orthoprocal, can be represented by this matrix. On the other hand, the abstract treatment of linear algebra presented later will give us a new insight into the structure of these matrices. The entries in our matrices will come from some arbitrary, but fixed, field K.","PeriodicalId":65610,"journal":{"name":"线性代数与矩阵理论研究进展(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80186639","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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