Bifurcation Analysis and Chaos Control in a Discrete-Time Predator-Prey System of Leslie Type with Simplified Holling Type IV Functional Response
The dynamic behavior of a discrete-time predator-prey system of Leslie type with simplified Holling type IV functional response is examined. We algebraically show that the system undergoes a bifurcation (flip or Neimark-Sacker) in the interior of R+2. Numerical simulations are presented not only to...
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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/10.1155/2017/9705985 |
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| author | S. M. Sohel Rana Umme Kulsum |
| author_facet | S. M. Sohel Rana Umme Kulsum |
| author_sort | S. M. Sohel Rana |
| collection | DOAJ |
| description | The dynamic behavior of a discrete-time predator-prey system of Leslie type with simplified Holling type IV functional response is examined. We algebraically show that the system undergoes a bifurcation (flip or Neimark-Sacker) in the interior of R+2. Numerical simulations are presented not only to validate analytical results but also to show chaotic behaviors which include bifurcations, phase portraits, period 2, 4, 6, 8, 10, and 20 orbits, invariant closed cycle, and attracting chaotic sets. Furthermore, we compute numerically maximum Lyapunov exponents and fractal dimension to justify the chaotic behaviors of the system. Finally, a strategy of feedback control is applied to stabilize chaos existing in the system. |
| format | Article |
| id | doaj-art-9eaa53909b914b26a26ca2e293e3a102 |
| 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-9eaa53909b914b26a26ca2e293e3a1022025-02-03T01:31:48ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2017-01-01201710.1155/2017/97059859705985Bifurcation Analysis and Chaos Control in a Discrete-Time Predator-Prey System of Leslie Type with Simplified Holling Type IV Functional ResponseS. M. Sohel Rana0Umme Kulsum1Department of Mathematics, University of Dhaka, Dhaka 1000, BangladeshDepartment of Computer Science and Engineering, University of Asia Pacific, Dhaka 1215, BangladeshThe dynamic behavior of a discrete-time predator-prey system of Leslie type with simplified Holling type IV functional response is examined. We algebraically show that the system undergoes a bifurcation (flip or Neimark-Sacker) in the interior of R+2. Numerical simulations are presented not only to validate analytical results but also to show chaotic behaviors which include bifurcations, phase portraits, period 2, 4, 6, 8, 10, and 20 orbits, invariant closed cycle, and attracting chaotic sets. Furthermore, we compute numerically maximum Lyapunov exponents and fractal dimension to justify the chaotic behaviors of the system. Finally, a strategy of feedback control is applied to stabilize chaos existing in the system.http://dx.doi.org/10.1155/2017/9705985 |
| spellingShingle | S. M. Sohel Rana Umme Kulsum Bifurcation Analysis and Chaos Control in a Discrete-Time Predator-Prey System of Leslie Type with Simplified Holling Type IV Functional Response Discrete Dynamics in Nature and Society |
| title | Bifurcation Analysis and Chaos Control in a Discrete-Time Predator-Prey System of Leslie Type with Simplified Holling Type IV Functional Response |
| title_full | Bifurcation Analysis and Chaos Control in a Discrete-Time Predator-Prey System of Leslie Type with Simplified Holling Type IV Functional Response |
| title_fullStr | Bifurcation Analysis and Chaos Control in a Discrete-Time Predator-Prey System of Leslie Type with Simplified Holling Type IV Functional Response |
| title_full_unstemmed | Bifurcation Analysis and Chaos Control in a Discrete-Time Predator-Prey System of Leslie Type with Simplified Holling Type IV Functional Response |
| title_short | Bifurcation Analysis and Chaos Control in a Discrete-Time Predator-Prey System of Leslie Type with Simplified Holling Type IV Functional Response |
| title_sort | bifurcation analysis and chaos control in a discrete time predator prey system of leslie type with simplified holling type iv functional response |
| url | http://dx.doi.org/10.1155/2017/9705985 |
| work_keys_str_mv | AT smsohelrana bifurcationanalysisandchaoscontrolinadiscretetimepredatorpreysystemofleslietypewithsimplifiedhollingtypeivfunctionalresponse AT ummekulsum bifurcationanalysisandchaoscontrolinadiscretetimepredatorpreysystemofleslietypewithsimplifiedhollingtypeivfunctionalresponse |