Pub Date : 2021-03-03DOI: 10.1080/14689367.2021.1872503
A. F. Fossi, J. Lubuma, C. Tadmon, B. Tsanou
ABSTRACT This work models, analyzes and assesses the impacts of environmental and spillover transmissions on Avian Influenza Virus (AIV) type A infection formulated in terms of nonlinear ordinary differential system that takes into account five spreading pathways: poultry-to-poultry; environment-to-poultry; poultry-to-human (spillover event); environment-to-human and poultry-to-environment. An in-depth theoretical and numerical analysis of the model is performed as follows. The basic reproduction number is computed and shown to be a sharp threshold for the global asymptotic dynamics of the submodel without recruitment of infected poultry. These results are obtained through the construction of suitable Lyapunov functions and the application of Poincaré-Bendixson combined with Lyapunov-LaSalle techniques. When the infected poultry is brought into the population, the model exhibits only a unique endemic equilibrium whose global asymptotic stability is established using the same techniques mentioned earlier. Further, the model is shown to exhibit a transcritical bifurcation with the value one of the basic reproduction number being the bifurcation parameter threshold. We further prove that during avian influenza outbreaks, the recruitment of infected poultry increases the disease endemic level. We show that the classical Runge-Kutta numerical method fails to preserve the positivity of solutions and alternatively design a nonstandard finite difference scheme (NSFD), which preserves the essential properties of the continuous system. Numerical simulations are implemented to illustrate the theoretical results and assess the role of the environmental and spillover transmissions on the disease.
{"title":"Mathematical modeling and nonstandard finite difference scheme analysis for the environmental and spillover transmissions of Avian Influenza A model","authors":"A. F. Fossi, J. Lubuma, C. Tadmon, B. Tsanou","doi":"10.1080/14689367.2021.1872503","DOIUrl":"https://doi.org/10.1080/14689367.2021.1872503","url":null,"abstract":"ABSTRACT This work models, analyzes and assesses the impacts of environmental and spillover transmissions on Avian Influenza Virus (AIV) type A infection formulated in terms of nonlinear ordinary differential system that takes into account five spreading pathways: poultry-to-poultry; environment-to-poultry; poultry-to-human (spillover event); environment-to-human and poultry-to-environment. An in-depth theoretical and numerical analysis of the model is performed as follows. The basic reproduction number is computed and shown to be a sharp threshold for the global asymptotic dynamics of the submodel without recruitment of infected poultry. These results are obtained through the construction of suitable Lyapunov functions and the application of Poincaré-Bendixson combined with Lyapunov-LaSalle techniques. When the infected poultry is brought into the population, the model exhibits only a unique endemic equilibrium whose global asymptotic stability is established using the same techniques mentioned earlier. Further, the model is shown to exhibit a transcritical bifurcation with the value one of the basic reproduction number being the bifurcation parameter threshold. We further prove that during avian influenza outbreaks, the recruitment of infected poultry increases the disease endemic level. We show that the classical Runge-Kutta numerical method fails to preserve the positivity of solutions and alternatively design a nonstandard finite difference scheme (NSFD), which preserves the essential properties of the continuous system. Numerical simulations are implemented to illustrate the theoretical results and assess the role of the environmental and spillover transmissions on the disease.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"36 1","pages":"212 - 255"},"PeriodicalIF":0.5,"publicationDate":"2021-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/14689367.2021.1872503","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42553929","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}
Pub Date : 2021-02-21DOI: 10.1080/14689367.2021.1872502
I. A. García
We study the problem of determining the canonical form that a planar analytic vector field in all the real plane can have to possess a given invariant analytic set. We determine some conditions that guarantee the only solution to this inverse problem is the trivial one.
{"title":"Some remarks on global analytic planar vector fields possessing an invariant analytic set","authors":"I. A. García","doi":"10.1080/14689367.2021.1872502","DOIUrl":"https://doi.org/10.1080/14689367.2021.1872502","url":null,"abstract":"We study the problem of determining the canonical form that a planar analytic vector field in all the real plane can have to possess a given invariant analytic set. We determine some conditions that guarantee the only solution to this inverse problem is the trivial one.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"36 1","pages":"204 - 211"},"PeriodicalIF":0.5,"publicationDate":"2021-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/14689367.2021.1872502","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49270556","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}
Pub Date : 2021-02-21DOI: 10.1080/14689367.2021.1875991
Adri'an Esparza-Amador, Mónica Moreno Rocha
ABSTRACT Consider a meromorphic function f with a countable compact set of essential singularities and whose Fatou set consists only of finitely many cycles of Leau domains and finitely many families of invariant Baker domains and their preimages. We provide sufficient conditions on a sequence of meromorphic functions with only Leau domains and uniformly convergent on compact sets to f, so that the Julia sets of converge in the Hausdorff metric to the Julia set of f. In particular, the Leau domains of approximate in the sense of Carathèodory, either the Leau or the Baker domains of f.
{"title":"Carathèodory convergence for Leau and Baker domains","authors":"Adri'an Esparza-Amador, Mónica Moreno Rocha","doi":"10.1080/14689367.2021.1875991","DOIUrl":"https://doi.org/10.1080/14689367.2021.1875991","url":null,"abstract":"ABSTRACT Consider a meromorphic function f with a countable compact set of essential singularities and whose Fatou set consists only of finitely many cycles of Leau domains and finitely many families of invariant Baker domains and their preimages. We provide sufficient conditions on a sequence of meromorphic functions with only Leau domains and uniformly convergent on compact sets to f, so that the Julia sets of converge in the Hausdorff metric to the Julia set of f. In particular, the Leau domains of approximate in the sense of Carathèodory, either the Leau or the Baker domains of f.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"36 1","pages":"256 - 276"},"PeriodicalIF":0.5,"publicationDate":"2021-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/14689367.2021.1875991","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48571326","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}
Pub Date : 2021-01-05DOI: 10.1080/14689367.2021.1933914
K. Burns, J. Buzzi, T. Fisher, Noelle Sawyer
We study the one parameter family of potential functions associated with the unstable Jacobian potential (or geometric potential) for the geodesic flow of a compact rank 1 surface of nonpositive curvature. For q<1, it is known that there is a unique equilibrium state associated with , and it has full support. For q>1 it is known that an invariant measure is an equilibrium state if and only if it is supported on the singular set. We study the critical value q = 1 and show that the ergodic equilibrium states are either the restriction to the regular set of the Liouville measure or measures supported on the singular set. In particular, when q = 1, there is a unique ergodic equilibrium state that gives positive measure to the regular set.
{"title":"Phase transitions for the geodesic flow of a rank one surface with nonpositive curvature","authors":"K. Burns, J. Buzzi, T. Fisher, Noelle Sawyer","doi":"10.1080/14689367.2021.1933914","DOIUrl":"https://doi.org/10.1080/14689367.2021.1933914","url":null,"abstract":"We study the one parameter family of potential functions associated with the unstable Jacobian potential (or geometric potential) for the geodesic flow of a compact rank 1 surface of nonpositive curvature. For q<1, it is known that there is a unique equilibrium state associated with , and it has full support. For q>1 it is known that an invariant measure is an equilibrium state if and only if it is supported on the singular set. We study the critical value q = 1 and show that the ergodic equilibrium states are either the restriction to the regular set of the Liouville measure or measures supported on the singular set. In particular, when q = 1, there is a unique ergodic equilibrium state that gives positive measure to the regular set.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"36 1","pages":"527 - 535"},"PeriodicalIF":0.5,"publicationDate":"2021-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/14689367.2021.1933914","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42694290","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}
Pub Date : 2020-12-29DOI: 10.1080/14689367.2023.2218601
Kengo Matsumoto
ABSTRACT We will characterize topologically conjugate one-sided topological Markov shifts in terms of their subgroups of continuous full groups and subalgebras of Cuntz–Krieger algebras.
{"title":"One-sided topological conjugacy of topological Markov shifts, continuous full groups and Cuntz–Krieger algebras","authors":"Kengo Matsumoto","doi":"10.1080/14689367.2023.2218601","DOIUrl":"https://doi.org/10.1080/14689367.2023.2218601","url":null,"abstract":"ABSTRACT We will characterize topologically conjugate one-sided topological Markov shifts in terms of their subgroups of continuous full groups and subalgebras of Cuntz–Krieger algebras.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"38 1","pages":"541 - 555"},"PeriodicalIF":0.5,"publicationDate":"2020-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43989136","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}
Pub Date : 2020-12-16DOI: 10.1080/14689367.2023.2206545
Mayara Antunes, B. Carvalho, Margoth Tacuri
In this paper, we study local stable/unstable sets of sensitive homeomorphisms with the shadowing property defined on compact metric spaces. We prove that local stable/unstable sets always contain a compact and perfect subset of the space. As a corollary, we generalize results in [Artigue et al. Beyond topological hyperbolicity: the Lshadowing property, J. Differ. Equ. 268(6) (2020), pp. 3057–3080.] and [Carvalho and Cordeiro, Positively N-expansive homeomorphisms and the L-shadowing property, J. Dyn. Differ. Equ. 31(2) (2019), pp. 1005–1016.] proving that positively countably expansive homeomorphisms defined on compact metric spaces satisfying either transitivity and the shadowing property, or the L-shadowing property, can only be defined in countable spaces.
{"title":"Sensitivity, local stable/unstable sets and shadowing","authors":"Mayara Antunes, B. Carvalho, Margoth Tacuri","doi":"10.1080/14689367.2023.2206545","DOIUrl":"https://doi.org/10.1080/14689367.2023.2206545","url":null,"abstract":"In this paper, we study local stable/unstable sets of sensitive homeomorphisms with the shadowing property defined on compact metric spaces. We prove that local stable/unstable sets always contain a compact and perfect subset of the space. As a corollary, we generalize results in [Artigue et al. Beyond topological hyperbolicity: the Lshadowing property, J. Differ. Equ. 268(6) (2020), pp. 3057–3080.] and [Carvalho and Cordeiro, Positively N-expansive homeomorphisms and the L-shadowing property, J. Dyn. Differ. Equ. 31(2) (2019), pp. 1005–1016.] proving that positively countably expansive homeomorphisms defined on compact metric spaces satisfying either transitivity and the shadowing property, or the L-shadowing property, can only be defined in countable spaces.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"38 1","pages":"477 - 489"},"PeriodicalIF":0.5,"publicationDate":"2020-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43884591","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}
Pub Date : 2020-12-10DOI: 10.1080/14689367.2020.1855416
Cao Zhao
Let be a topologically mixing subshift of finite type on an alphabet consisting of m symbols. Let be a continuous function. For a positive function and a continuous positive function , define the sets of recurrence points and In this paper, we give quantitative estimates of the sets of recurrence points, that is, can be expressed by ψ and is the solution of the Bowen equation of topological pressure.
{"title":"Quantitative recurrence properties in the historic set for symbolic systems","authors":"Cao Zhao","doi":"10.1080/14689367.2020.1855416","DOIUrl":"https://doi.org/10.1080/14689367.2020.1855416","url":null,"abstract":"Let be a topologically mixing subshift of finite type on an alphabet consisting of m symbols. Let be a continuous function. For a positive function and a continuous positive function , define the sets of recurrence points and In this paper, we give quantitative estimates of the sets of recurrence points, that is, can be expressed by ψ and is the solution of the Bowen equation of topological pressure.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"36 1","pages":"181 - 203"},"PeriodicalIF":0.5,"publicationDate":"2020-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/14689367.2020.1855416","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45821503","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}
Pub Date : 2020-12-06DOI: 10.1080/14689367.2020.1849031
G. Blé, F. E. Castillo-Santos, D. González, R. Valdez
ABSTRACT We consider a family of quartic polynomials generated by the composition of two quadratic polynomials. The elements of this family have two complex parameters, however they have at most two dynamic behaviors, since every map in this family have two critical points with the same forward orbits. In this paper, we study this quartic family in the complex parameter space, and we describe the dynamical plane for some special parameters. Moreover, we analyze the parameter space for these quartic polynomials with a super attracting fixed point. We describe the connectedness locus for this family, and we prove the locally connectedness of the boundary of hyperbolic components in the parameter space.
{"title":"On a quartic polynomials family of two parameters","authors":"G. Blé, F. E. Castillo-Santos, D. González, R. Valdez","doi":"10.1080/14689367.2020.1849031","DOIUrl":"https://doi.org/10.1080/14689367.2020.1849031","url":null,"abstract":"ABSTRACT We consider a family of quartic polynomials generated by the composition of two quadratic polynomials. The elements of this family have two complex parameters, however they have at most two dynamic behaviors, since every map in this family have two critical points with the same forward orbits. In this paper, we study this quartic family in the complex parameter space, and we describe the dynamical plane for some special parameters. Moreover, we analyze the parameter space for these quartic polynomials with a super attracting fixed point. We describe the connectedness locus for this family, and we prove the locally connectedness of the boundary of hyperbolic components in the parameter space.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"36 1","pages":"154 - 166"},"PeriodicalIF":0.5,"publicationDate":"2020-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/14689367.2020.1849031","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44264369","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}
Pub Date : 2020-12-06DOI: 10.1080/14689367.2020.1853061
J. Giné, C. Valls
ABSTRACT We provide the sufficient conditions for the simultaneous existence of centres for two families of planar double-reversible quintic systems. Computing the focal values and using crossed resultants and Gröbner bases, we find the centre conditions for such systems. The results obtained show that there exist a kind of symmetry where the number of centers in a quintic system is more than 5, so higher than the degree of the system. This fact gives a counterexample to the question posed in a previous work.
{"title":"Simultaneity of centres in double-reversible planar differential systems","authors":"J. Giné, C. Valls","doi":"10.1080/14689367.2020.1853061","DOIUrl":"https://doi.org/10.1080/14689367.2020.1853061","url":null,"abstract":"ABSTRACT We provide the sufficient conditions for the simultaneous existence of centres for two families of planar double-reversible quintic systems. Computing the focal values and using crossed resultants and Gröbner bases, we find the centre conditions for such systems. The results obtained show that there exist a kind of symmetry where the number of centers in a quintic system is more than 5, so higher than the degree of the system. This fact gives a counterexample to the question posed in a previous work.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"36 1","pages":"167 - 180"},"PeriodicalIF":0.5,"publicationDate":"2020-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/14689367.2020.1853061","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45997270","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}
Pub Date : 2020-11-29DOI: 10.1080/14689367.2020.1844154
Qianqian Yang, Shuailing Wang
For any , let be the β-transformation dynamical system. For any , define the distal set of a given point y as Yang, Li, et al. [15] proved that the Hausdorff dimension of the distal set of any point is one for any β>1. In this paper, we study the winning property of the distal set of a given point y. We prove that the distal set of a given point y is α-winning for any and , where is a constant. By the definition of winning set, it's obvious that the distal set of a given point y is a dense set.
对于任意，设为β-变换动力系统。对于任意，定义给定点y的远端集为Yang, Li, et al.[15]证明了任意点的远端集的Hausdorff维数对于任意β>1为1。本文研究了给定点y的远端集合的致胜性质，证明了给定点y的远端集合对任意和都是α-致胜的，其中为常数。根据获胜集的定义，可以明显地看出，给定点y的远端集是一个稠密集。
{"title":"Winning property of distal set for β-transformations","authors":"Qianqian Yang, Shuailing Wang","doi":"10.1080/14689367.2020.1844154","DOIUrl":"https://doi.org/10.1080/14689367.2020.1844154","url":null,"abstract":"For any , let be the β-transformation dynamical system. For any , define the distal set of a given point y as Yang, Li, et al. [15] proved that the Hausdorff dimension of the distal set of any point is one for any β>1. In this paper, we study the winning property of the distal set of a given point y. We prove that the distal set of a given point y is α-winning for any and , where is a constant. By the definition of winning set, it's obvious that the distal set of a given point y is a dense set.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"36 1","pages":"128 - 141"},"PeriodicalIF":0.5,"publicationDate":"2020-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/14689367.2020.1844154","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48258574","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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