Bifurcation Analysis and Chaos Control in a Discrete-Time Parasite-Host Model
A discrete-time parasite-host system with bifurcation is investigated in detail in this paper. The existence and stability of nonnegative fixed points are explored and the conditions for the existence of flip bifurcation and Neimark-Sacker bifurcation are derived by using the center manifold theorem...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2017/9275474 |
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| _version_ | 1832546010067369984 |
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| author | Xueli Chen Lishun Ren |
| author_facet | Xueli Chen Lishun Ren |
| author_sort | Xueli Chen |
| collection | DOAJ |
| description | A discrete-time parasite-host system with bifurcation is investigated in detail in this paper. The existence and stability of nonnegative fixed points are explored and the conditions for the existence of flip bifurcation and Neimark-Sacker bifurcation are derived by using the center manifold theorem and bifurcation theory. And we also prove the chaos in the sense of Marotto. The numerical simulations not only illustrate the consistence with the theoretical analysis, but also exhibit other complex dynamical behaviors, such as bifurcation diagrams, Maximum Lyapunov exponents, and phase portraits. More specifically, when the integral step size is chosen as a bifurcation parameter, this paper presents the finding of period orbits, attracting invariant cycles and chaotic attractors of the discrete-time parasite-host system. Specifically, we have stabilized the chaotic orbits at an unstable fixed point by using the feedback control method. |
| format | Article |
| id | doaj-art-b4fe03f567f24224ac81f9c71f5b5a29 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-b4fe03f567f24224ac81f9c71f5b5a292025-02-03T07:24:10ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2017-01-01201710.1155/2017/92754749275474Bifurcation Analysis and Chaos Control in a Discrete-Time Parasite-Host ModelXueli Chen0Lishun Ren1Department of Mathematics and Statistics, Zhoukou Normal University, Zhoukou, Henan 466000, ChinaDepartment of Mathematics and Statistics, Zhoukou Normal University, Zhoukou, Henan 466000, ChinaA discrete-time parasite-host system with bifurcation is investigated in detail in this paper. The existence and stability of nonnegative fixed points are explored and the conditions for the existence of flip bifurcation and Neimark-Sacker bifurcation are derived by using the center manifold theorem and bifurcation theory. And we also prove the chaos in the sense of Marotto. The numerical simulations not only illustrate the consistence with the theoretical analysis, but also exhibit other complex dynamical behaviors, such as bifurcation diagrams, Maximum Lyapunov exponents, and phase portraits. More specifically, when the integral step size is chosen as a bifurcation parameter, this paper presents the finding of period orbits, attracting invariant cycles and chaotic attractors of the discrete-time parasite-host system. Specifically, we have stabilized the chaotic orbits at an unstable fixed point by using the feedback control method.http://dx.doi.org/10.1155/2017/9275474 |
| spellingShingle | Xueli Chen Lishun Ren Bifurcation Analysis and Chaos Control in a Discrete-Time Parasite-Host Model Discrete Dynamics in Nature and Society |
| title | Bifurcation Analysis and Chaos Control in a Discrete-Time Parasite-Host Model |
| title_full | Bifurcation Analysis and Chaos Control in a Discrete-Time Parasite-Host Model |
| title_fullStr | Bifurcation Analysis and Chaos Control in a Discrete-Time Parasite-Host Model |
| title_full_unstemmed | Bifurcation Analysis and Chaos Control in a Discrete-Time Parasite-Host Model |
| title_short | Bifurcation Analysis and Chaos Control in a Discrete-Time Parasite-Host Model |
| title_sort | bifurcation analysis and chaos control in a discrete time parasite host model |
| url | http://dx.doi.org/10.1155/2017/9275474 |
| work_keys_str_mv | AT xuelichen bifurcationanalysisandchaoscontrolinadiscretetimeparasitehostmodel AT lishunren bifurcationanalysisandchaoscontrolinadiscretetimeparasitehostmodel |