Dynamical analysis of a giving up smoking model with time delay
Abstract In this paper, we are concerned with a delayed smoking model in which the population is divided into five classes. Sufficient conditions guaranteeing the local stability and existence of Hopf bifurcation for the model are established by taking the time delay as a bifurcation parameter and e...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-12-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13662-019-2450-4 |
| _version_ | 1818352653079412736 |
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| author | Zizhen Zhang Ruibin Wei Wanjun Xia |
| author_facet | Zizhen Zhang Ruibin Wei Wanjun Xia |
| author_sort | Zizhen Zhang |
| collection | DOAJ |
| description | Abstract In this paper, we are concerned with a delayed smoking model in which the population is divided into five classes. Sufficient conditions guaranteeing the local stability and existence of Hopf bifurcation for the model are established by taking the time delay as a bifurcation parameter and employing the Routh–Hurwitz criteria. Furthermore, direction and stability of the Hopf bifurcation are investigated by applying the center manifold theorem and normal form theory. Finally, computer simulations are implemented to support the analytic results and to analyze the effects of some parameters on the dynamical behavior of the model. |
| first_indexed | 2024-12-13T18:57:03Z |
| format | Article |
| id | doaj.art-f5d90f422c65447abaa3dcbeba17c002 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-13T18:57:03Z |
| publishDate | 2019-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-f5d90f422c65447abaa3dcbeba17c0022022-12-21T23:34:47ZengSpringerOpenAdvances in Difference Equations1687-18472019-12-012019111710.1186/s13662-019-2450-4Dynamical analysis of a giving up smoking model with time delayZizhen Zhang0Ruibin Wei1Wanjun Xia2School of Management Science and Engineering, Anhui University of Finance and EconomicsSchool of Management Science and Engineering, Anhui University of Finance and EconomicsSchool of Management Science and Engineering, Anhui University of Finance and EconomicsAbstract In this paper, we are concerned with a delayed smoking model in which the population is divided into five classes. Sufficient conditions guaranteeing the local stability and existence of Hopf bifurcation for the model are established by taking the time delay as a bifurcation parameter and employing the Routh–Hurwitz criteria. Furthermore, direction and stability of the Hopf bifurcation are investigated by applying the center manifold theorem and normal form theory. Finally, computer simulations are implemented to support the analytic results and to analyze the effects of some parameters on the dynamical behavior of the model.https://doi.org/10.1186/s13662-019-2450-4DelayHopf bifurcationStabilitySmoking model |
| spellingShingle | Zizhen Zhang Ruibin Wei Wanjun Xia Dynamical analysis of a giving up smoking model with time delay Advances in Difference Equations Delay Hopf bifurcation Stability Smoking model |
| title | Dynamical analysis of a giving up smoking model with time delay |
| title_full | Dynamical analysis of a giving up smoking model with time delay |
| title_fullStr | Dynamical analysis of a giving up smoking model with time delay |
| title_full_unstemmed | Dynamical analysis of a giving up smoking model with time delay |
| title_short | Dynamical analysis of a giving up smoking model with time delay |
| title_sort | dynamical analysis of a giving up smoking model with time delay |
| topic | Delay Hopf bifurcation Stability Smoking model |
| url | https://doi.org/10.1186/s13662-019-2450-4 |
| work_keys_str_mv | AT zizhenzhang dynamicalanalysisofagivingupsmokingmodelwithtimedelay AT ruibinwei dynamicalanalysisofagivingupsmokingmodelwithtimedelay AT wanjunxia dynamicalanalysisofagivingupsmokingmodelwithtimedelay |