Bifurcations and Structures of the Parameter Space of a Discrete-Time SIS Epidemic Model
The dynamics of a discrete-time SIS epidemic model are reported in this paper. Three types of codimension one bifurcation, namely, transcritical, flip, Neimark–Sacker (N-S) bifurcations, and their intersection codimension two bifurcations including 1 : 2, 1 : 3, and 1 : 4 resonances are discussed. T...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/2233452 |
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| author | Yun Liu Xijuan Liu |
| author_facet | Yun Liu Xijuan Liu |
| author_sort | Yun Liu |
| collection | DOAJ |
| description | The dynamics of a discrete-time SIS epidemic model are reported in this paper. Three types of codimension one bifurcation, namely, transcritical, flip, Neimark–Sacker (N-S) bifurcations, and their intersection codimension two bifurcations including 1 : 2, 1 : 3, and 1 : 4 resonances are discussed. The necessary and sufficient conditions for detecting these types of bifurcation are derived using algebraic criterion methods. Numerical simulations are conducted not only to illustrate analytical results but also to exhibit complex behaviors which include period-doubling bifurcation in period −2,−4,−8,−16 orbits, invariant closed cycles, and attracting chaotic sets. Especially, here we investigate the parameter space of the discrete model. We also investigate the organization of typical periodic structures embedded in a quasiperiodic region. We identify period-adding, Farey sequence of periodic structures embedded in this quasiperiodic region. |
| format | Article |
| id | doaj-art-98b71db3c1844caa86c663863387a5c0 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-98b71db3c1844caa86c663863387a5c02025-02-03T05:53:40ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/2233452Bifurcations and Structures of the Parameter Space of a Discrete-Time SIS Epidemic ModelYun Liu0Xijuan Liu1College of Information EngineeringCollege of Information EngineeringThe dynamics of a discrete-time SIS epidemic model are reported in this paper. Three types of codimension one bifurcation, namely, transcritical, flip, Neimark–Sacker (N-S) bifurcations, and their intersection codimension two bifurcations including 1 : 2, 1 : 3, and 1 : 4 resonances are discussed. The necessary and sufficient conditions for detecting these types of bifurcation are derived using algebraic criterion methods. Numerical simulations are conducted not only to illustrate analytical results but also to exhibit complex behaviors which include period-doubling bifurcation in period −2,−4,−8,−16 orbits, invariant closed cycles, and attracting chaotic sets. Especially, here we investigate the parameter space of the discrete model. We also investigate the organization of typical periodic structures embedded in a quasiperiodic region. We identify period-adding, Farey sequence of periodic structures embedded in this quasiperiodic region.http://dx.doi.org/10.1155/2022/2233452 |
| spellingShingle | Yun Liu Xijuan Liu Bifurcations and Structures of the Parameter Space of a Discrete-Time SIS Epidemic Model Journal of Mathematics |
| title | Bifurcations and Structures of the Parameter Space of a Discrete-Time SIS Epidemic Model |
| title_full | Bifurcations and Structures of the Parameter Space of a Discrete-Time SIS Epidemic Model |
| title_fullStr | Bifurcations and Structures of the Parameter Space of a Discrete-Time SIS Epidemic Model |
| title_full_unstemmed | Bifurcations and Structures of the Parameter Space of a Discrete-Time SIS Epidemic Model |
| title_short | Bifurcations and Structures of the Parameter Space of a Discrete-Time SIS Epidemic Model |
| title_sort | bifurcations and structures of the parameter space of a discrete time sis epidemic model |
| url | http://dx.doi.org/10.1155/2022/2233452 |
| work_keys_str_mv | AT yunliu bifurcationsandstructuresoftheparameterspaceofadiscretetimesisepidemicmodel AT xijuanliu bifurcationsandstructuresoftheparameterspaceofadiscretetimesisepidemicmodel |