We consider a predator-prey model with a non-monotonic functional response encompassing a prey refuge and a strong Allee effect on the prey. The multiple existence and stability of interior equilibria are investigated. The bifurcation analysis shows this model can exhibit numerous kinds of bifurcations (e.g., saddle-node, Hopf-Andronov and Bogdanov-Takens bifurcations). It is found that there exist diverse parameter values for which the model exhibits a limit cycle, a homoclinic orbit, and even many heteroclinic curves. The results obtained reveal the prey refuge in the model brings rich dynamics and makes the system more sensitive to parameter values. The main purpose of the present work is to offer a complete mathematical analysis of the effect that the refuge brings about.
{"title":"Dynamical complexity of a predator-prey model with a prey refuge and Allee effect","authors":"JIANPING GAO, JIANGHONG ZHANG, WENYAN LIAN","doi":"10.55730/1300-0098.3481","DOIUrl":"https://doi.org/10.55730/1300-0098.3481","url":null,"abstract":"We consider a predator-prey model with a non-monotonic functional response encompassing a prey refuge and a strong Allee effect on the prey. The multiple existence and stability of interior equilibria are investigated. The bifurcation analysis shows this model can exhibit numerous kinds of bifurcations (e.g., saddle-node, Hopf-Andronov and Bogdanov-Takens bifurcations). It is found that there exist diverse parameter values for which the model exhibits a limit cycle, a homoclinic orbit, and even many heteroclinic curves. The results obtained reveal the prey refuge in the model brings rich dynamics and makes the system more sensitive to parameter values. The main purpose of the present work is to offer a complete mathematical analysis of the effect that the refuge brings about.","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":" 13","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135292628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
: Given an indexed family { ( S i , · i , ≤ i ) , i ∈ I } of disjoint ordered semigroups, we construct an ordered semigroup having ( S i , · i , ≤ i ) , i ∈ I as subsemigroups (with respect to the operation and order relation of each ( S i , · i , ≤ i ) , i ∈ I ). This ordered semigroup is the free ordered product Π i ∈ I ∗ S i of the family { S i , i ∈ I } and we give the crucial property which essentially characterizes the free products. Next we study the same problem in the case that the family { ( S i , · i , ≤ i ) , i ∈ I } of ordered semigroups has as intersection the ordered semigroup ( U, · U , ≤ U ) which is a subsemigroup of ( S i , · i , ≤ i ) for every i ∈ I (with respect to the operation and order relation of each ( S i , · i , ≤ i ) , i ∈ I ). To do this, we first consider the ordered semigroup amalgam A = [ { ( S i , · i , ≤ i ) , i ∈ I } ; ( U, · U , ≤ U ) ; { φ i : U → S i , i ∈ I } ] (where { φ i : U → S i , i ∈ I } is a family of monomorphisms) and then we construct the free ordered product Π ∗ U i ∈ I S i of the ordered semigroup amalgam A considering the ordered quotient of the free ordered product Π i ∈ I ∗ S i by an appropriate pseudoorder of Π i ∈ I ∗ S i through which for each i, j ∈ I and for each u ∈ U , φ i ( u ) ∈ S i is identified (by means of monomorphisms) with φ j ( u ) ∈ S j . We give a sufficient and necessary condition so that an ordered semigroup amalgam is embedded in an ordered semigroup. At the end of the paper, we introduce the notion of ordered dominions. An element d of an ordered semigroup S is dominated by a subsemigroup U of S if for all ordered semigroups ( T, · , ≤ ) and for all homomorphisms β, γ : S → T such that β ( u ) = γ ( u ) for each u ∈ U , we have [ β ( d )) T ≤ ∩ [ γ ( d )) T ≤ ̸ = ∅ . In the last Theorem of the paper, we give an expression of the set of elements of S dominated by U based on ordered semigroup amalgams.
{"title":"Free ordered products-ordered semigroup amalgams-ordered dominions","authors":"MICHAEL TSINGELIS","doi":"10.55730/1300-0098.3468","DOIUrl":"https://doi.org/10.55730/1300-0098.3468","url":null,"abstract":": Given an indexed family { ( S i , · i , ≤ i ) , i ∈ I } of disjoint ordered semigroups, we construct an ordered semigroup having ( S i , · i , ≤ i ) , i ∈ I as subsemigroups (with respect to the operation and order relation of each ( S i , · i , ≤ i ) , i ∈ I ). This ordered semigroup is the free ordered product Π i ∈ I ∗ S i of the family { S i , i ∈ I } and we give the crucial property which essentially characterizes the free products. Next we study the same problem in the case that the family { ( S i , · i , ≤ i ) , i ∈ I } of ordered semigroups has as intersection the ordered semigroup ( U, · U , ≤ U ) which is a subsemigroup of ( S i , · i , ≤ i ) for every i ∈ I (with respect to the operation and order relation of each ( S i , · i , ≤ i ) , i ∈ I ). To do this, we first consider the ordered semigroup amalgam A = [ { ( S i , · i , ≤ i ) , i ∈ I } ; ( U, · U , ≤ U ) ; { φ i : U → S i , i ∈ I } ] (where { φ i : U → S i , i ∈ I } is a family of monomorphisms) and then we construct the free ordered product Π ∗ U i ∈ I S i of the ordered semigroup amalgam A considering the ordered quotient of the free ordered product Π i ∈ I ∗ S i by an appropriate pseudoorder of Π i ∈ I ∗ S i through which for each i, j ∈ I and for each u ∈ U , φ i ( u ) ∈ S i is identified (by means of monomorphisms) with φ j ( u ) ∈ S j . We give a sufficient and necessary condition so that an ordered semigroup amalgam is embedded in an ordered semigroup. At the end of the paper, we introduce the notion of ordered dominions. An element d of an ordered semigroup S is dominated by a subsemigroup U of S if for all ordered semigroups ( T, · , ≤ ) and for all homomorphisms β, γ : S → T such that β ( u ) = γ ( u ) for each u ∈ U , we have [ β ( d )) T ≤ ∩ [ γ ( d )) T ≤ ̸ = ∅ . In the last Theorem of the paper, we give an expression of the set of elements of S dominated by U based on ordered semigroup amalgams.","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":" 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135292633","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this extensive note, various differential-type operators in certain domains of the complex plane will be first introduced, a number of their comprehensive characteristic properties will be next pointed out and an extensive theorem dealing with some argument properties for several multivalent(ly) analytic functions will be also presented. In addition, numerous implications and suggestions, which can be obtained with the help of general result, will be determined.
{"title":"An extensive note on characteristic properties and possible implications of some operators designated by various type derivatives","authors":"ÖMER FARUK KULALI, HÜSEYİN IRMAK","doi":"10.55730/1300-0098.3470","DOIUrl":"https://doi.org/10.55730/1300-0098.3470","url":null,"abstract":"In this extensive note, various differential-type operators in certain domains of the complex plane will be first introduced, a number of their comprehensive characteristic properties will be next pointed out and an extensive theorem dealing with some argument properties for several multivalent(ly) analytic functions will be also presented. In addition, numerous implications and suggestions, which can be obtained with the help of general result, will be determined.","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":" 21","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135292620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the existence of $6$-cycles for some families of difference equations of third order","authors":"ANTONIO LINERO BAS, DANIEL NIEVES ROLDÁN","doi":"10.55730/1300-0098.3480","DOIUrl":"https://doi.org/10.55730/1300-0098.3480","url":null,"abstract":"","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":" 14","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135292627","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The present paper is devoted to a scheme-theoretic analog of the Fredholm theory. The continuity of the index function over the coordinate ring of an algebraic variety is investigated. It turns out that the index is closely related to the filtered topology given by finite products of maximal ideals. We prove that a variety over a field possesses the index function on nonzero elements of its coordinate ring iff it is an algebraic curve. In this case, the index is obtained by means of the multiplicity function from its normalization if the ground field is algebraically closed.
{"title":"Operator index of a nonsingular algebraic curve","authors":"ANAR DOSİ","doi":"10.55730/1300-0098.3477","DOIUrl":"https://doi.org/10.55730/1300-0098.3477","url":null,"abstract":"The present paper is devoted to a scheme-theoretic analog of the Fredholm theory. The continuity of the index function over the coordinate ring of an algebraic variety is investigated. It turns out that the index is closely related to the filtered topology given by finite products of maximal ideals. We prove that a variety over a field possesses the index function on nonzero elements of its coordinate ring iff it is an algebraic curve. In this case, the index is obtained by means of the multiplicity function from its normalization if the ground field is algebraically closed.","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":" 12","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135292629","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We discuss dynamical systems that exhibit at least one weakly asymptotically periodic point. In the general case we prove that the system becomes trivial (it is either a periodic point or a fixed point) provided it is equicontinuous and transitive. This result can be used to provide a simple characterization of periodic points in transitive systems. We also discuss systems whose orbits are both proximal and weakly asymptotically periodic. As a result, we obtain a more general tool to detect mutual dynamics between two close orbits which need not be bounded (or have the empty limit set).
{"title":"Proximality and transitivity in relation to points that are asymptotic to themselves","authors":"KAROL GRYSZKA","doi":"10.55730/1300-0098.3476","DOIUrl":"https://doi.org/10.55730/1300-0098.3476","url":null,"abstract":"We discuss dynamical systems that exhibit at least one weakly asymptotically periodic point. In the general case we prove that the system becomes trivial (it is either a periodic point or a fixed point) provided it is equicontinuous and transitive. This result can be used to provide a simple characterization of periodic points in transitive systems. We also discuss systems whose orbits are both proximal and weakly asymptotically periodic. As a result, we obtain a more general tool to detect mutual dynamics between two close orbits which need not be bounded (or have the empty limit set).","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":" 27","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135292749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 establish the eigenvalues and the eigenfunctions of both the $q$-Durrmeyer operators $D_{n,q}$ and the limit $q$-Durrmeyer operators $D_{infty,q}$ introduced by V. Gupta in the case 0<$q$<1. All moments for $D_{n,q}$ and $D_{infty,q}$ are provided. The coefficients for the eigenfunctions of the operators are explicitly derived and the eigenfunctions of these operators are illustrated by graphical examples.
{"title":"On the eigenstructure of the $q$-Durrmeyer operators","authors":"ÖVGÜ GÜREL YILMAZ","doi":"10.55730/1300-0098.3454","DOIUrl":"https://doi.org/10.55730/1300-0098.3454","url":null,"abstract":"The purpose of this paper is to establish the eigenvalues and the eigenfunctions of both the $q$-Durrmeyer operators $D_{n,q}$ and the limit $q$-Durrmeyer operators $D_{infty,q}$ introduced by V. Gupta in the case 0<$q$<1. All moments for $D_{n,q}$ and $D_{infty,q}$ are provided. The coefficients for the eigenfunctions of the operators are explicitly derived and the eigenfunctions of these operators are illustrated by graphical examples.","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135865223","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Several recent papers were devoted to various modifications of limited, Grothendieck, and Dunford-Pettis operators, etc., through involving the Banach lattice structure. In the present paper, it is shown that many of these operators appear as operators affiliated to well-known properties of Banach lattices, like the disjoint (dual) Schur property, the disjoint Grothendieck property, the property (d), the sequential w$^ast$-continuity of the lattice operations, etc. We also introduce new classes of operators such as the s-GPP-operators, s-BDP-operators, and bi-sP-operators. It is proved that the spaces consisting of regular versions of the above-mentioned operators are all the Banach spaces. The domination problem for these operators is investigated.
{"title":"Operators affiliated to Banach lattice properties and their enveloping norms","authors":"EDUARD EMELYANOV, SVETLANA GOROKHOVA","doi":"10.55730/1300-0098.3455","DOIUrl":"https://doi.org/10.55730/1300-0098.3455","url":null,"abstract":"Several recent papers were devoted to various modifications of limited, Grothendieck, and Dunford-Pettis operators, etc., through involving the Banach lattice structure. In the present paper, it is shown that many of these operators appear as operators affiliated to well-known properties of Banach lattices, like the disjoint (dual) Schur property, the disjoint Grothendieck property, the property (d), the sequential w$^ast$-continuity of the lattice operations, etc. We also introduce new classes of operators such as the s-GPP-operators, s-BDP-operators, and bi-sP-operators. It is proved that the spaces consisting of regular versions of the above-mentioned operators are all the Banach spaces. The domination problem for these operators is investigated.","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":"71 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135865217","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we investigate the existence of positive periodic solutions of a third-order nonlinear integro-differential equation with distributed delays, by using the Green function and the Krasnosel'skii fixed point theorem in cones of Banach spaces, providing new results on this field. Three examples are analyzed to illustrate the effectiveness of the abstract results.
{"title":"On positive periodic solutions to third-order integro-differential equations with distributed delays","authors":"MIMIA BENHADRI, TOMAS CARABALLO","doi":"10.55730/1300-0098.3465","DOIUrl":"https://doi.org/10.55730/1300-0098.3465","url":null,"abstract":"In this paper, we investigate the existence of positive periodic solutions of a third-order nonlinear integro-differential equation with distributed delays, by using the Green function and the Krasnosel'skii fixed point theorem in cones of Banach spaces, providing new results on this field. Three examples are analyzed to illustrate the effectiveness of the abstract results.","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135865216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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