Chaotic Dynamics and Control of Discrete Ratio-Dependent Predator-Prey System
This study examines the complexity of a discrete-time predator-prey system with ratio-dependent functional response. We establish algebraically the conditions for existence of fixed points and their stability. We show that under some parametric conditions the system passes through a bifurcation (fli...
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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/10.1155/2017/4537450 |
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| _version_ | 1849398212999249920 |
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| author | Sarker Md. Sohel Rana |
| author_facet | Sarker Md. Sohel Rana |
| author_sort | Sarker Md. Sohel Rana |
| collection | DOAJ |
| description | This study examines the complexity of a discrete-time predator-prey system with ratio-dependent functional response. We establish algebraically the conditions for existence of fixed points and their stability. We show that under some parametric conditions the system passes through a bifurcation (flip or Neimark-Sacker). Numerical simulations are presented not only to justify theoretical results but also to exhibit new complex behaviors which include phase portraits, orbits of periods 9, 19, and 26, invariant closed circle, and attracting chaotic sets. Moreover, we measure numerically the Lyapunov exponents and fractal dimension to confirm the chaotic dynamics of the system. Finally, a state feedback control method is applied to control chaos which exists in the system. |
| format | Article |
| id | doaj-art-9e7d20f70206405c8261a0bc0907be5f |
| 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-9e7d20f70206405c8261a0bc0907be5f2025-08-20T03:38:40ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2017-01-01201710.1155/2017/45374504537450Chaotic Dynamics and Control of Discrete Ratio-Dependent Predator-Prey SystemSarker Md. Sohel Rana0Department of Mathematics, University of Dhaka, Dhaka 1000, BangladeshThis study examines the complexity of a discrete-time predator-prey system with ratio-dependent functional response. We establish algebraically the conditions for existence of fixed points and their stability. We show that under some parametric conditions the system passes through a bifurcation (flip or Neimark-Sacker). Numerical simulations are presented not only to justify theoretical results but also to exhibit new complex behaviors which include phase portraits, orbits of periods 9, 19, and 26, invariant closed circle, and attracting chaotic sets. Moreover, we measure numerically the Lyapunov exponents and fractal dimension to confirm the chaotic dynamics of the system. Finally, a state feedback control method is applied to control chaos which exists in the system.http://dx.doi.org/10.1155/2017/4537450 |
| spellingShingle | Sarker Md. Sohel Rana Chaotic Dynamics and Control of Discrete Ratio-Dependent Predator-Prey System Discrete Dynamics in Nature and Society |
| title | Chaotic Dynamics and Control of Discrete Ratio-Dependent Predator-Prey System |
| title_full | Chaotic Dynamics and Control of Discrete Ratio-Dependent Predator-Prey System |
| title_fullStr | Chaotic Dynamics and Control of Discrete Ratio-Dependent Predator-Prey System |
| title_full_unstemmed | Chaotic Dynamics and Control of Discrete Ratio-Dependent Predator-Prey System |
| title_short | Chaotic Dynamics and Control of Discrete Ratio-Dependent Predator-Prey System |
| title_sort | chaotic dynamics and control of discrete ratio dependent predator prey system |
| url | http://dx.doi.org/10.1155/2017/4537450 |
| work_keys_str_mv | AT sarkermdsohelrana chaoticdynamicsandcontrolofdiscreteratiodependentpredatorpreysystem |