The Bifurcation of Two Invariant Closed Curves in a Discrete Model
A discrete population model integrated using the forward Euler method is investigated. The qualitative bifurcation analysis indicates that the model exhibits rich dynamical behaviors including the existence of the equilibrium state, the flip bifurcation, the Neimark-Sacker bifurcation, and two invar...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2018/1613709 |
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| _version_ | 1832561655478747136 |
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| author | Yingying Zhang Yicang Zhou |
| author_facet | Yingying Zhang Yicang Zhou |
| author_sort | Yingying Zhang |
| collection | DOAJ |
| description | A discrete population model integrated using the forward Euler method is investigated. The qualitative bifurcation analysis indicates that the model exhibits rich dynamical behaviors including the existence of the equilibrium state, the flip bifurcation, the Neimark-Sacker bifurcation, and two invariant closed curves. The conditions for existence of these bifurcations are derived by using the center manifold and bifurcation theory. Numerical simulations and bifurcation diagrams exhibit the complex dynamical behaviors, especially the occurrence of two invariant closed curves. |
| format | Article |
| id | doaj-art-9fcacf2520424c9fa6ca9cd29c146132 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-9fcacf2520424c9fa6ca9cd29c1461322025-02-03T01:24:34ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2018-01-01201810.1155/2018/16137091613709The Bifurcation of Two Invariant Closed Curves in a Discrete ModelYingying Zhang0Yicang Zhou1School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, ChinaSchool of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, ChinaA discrete population model integrated using the forward Euler method is investigated. The qualitative bifurcation analysis indicates that the model exhibits rich dynamical behaviors including the existence of the equilibrium state, the flip bifurcation, the Neimark-Sacker bifurcation, and two invariant closed curves. The conditions for existence of these bifurcations are derived by using the center manifold and bifurcation theory. Numerical simulations and bifurcation diagrams exhibit the complex dynamical behaviors, especially the occurrence of two invariant closed curves.http://dx.doi.org/10.1155/2018/1613709 |
| spellingShingle | Yingying Zhang Yicang Zhou The Bifurcation of Two Invariant Closed Curves in a Discrete Model Discrete Dynamics in Nature and Society |
| title | The Bifurcation of Two Invariant Closed Curves in a Discrete Model |
| title_full | The Bifurcation of Two Invariant Closed Curves in a Discrete Model |
| title_fullStr | The Bifurcation of Two Invariant Closed Curves in a Discrete Model |
| title_full_unstemmed | The Bifurcation of Two Invariant Closed Curves in a Discrete Model |
| title_short | The Bifurcation of Two Invariant Closed Curves in a Discrete Model |
| title_sort | bifurcation of two invariant closed curves in a discrete model |
| url | http://dx.doi.org/10.1155/2018/1613709 |
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