Dynamical Complexities of a Discrete Ivlev-Type Predator-Prey System
In this study, we examine a discrete predator-prey system from the following two perspectives: (i) the functional response is of the Ivlev type and (ii) the prey growth rate is of the Gompertz type. We define the stability requirement for feasible fixed points. We demonstrate algebraically that if t...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2023-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2023/4555469 |
| _version_ | 1811158692075143168 |
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| author | Sarker Md. Sohel Rana |
| author_facet | Sarker Md. Sohel Rana |
| author_sort | Sarker Md. Sohel Rana |
| collection | DOAJ |
| description | In this study, we examine a discrete predator-prey system from the following two perspectives: (i) the functional response is of the Ivlev type and (ii) the prey growth rate is of the Gompertz type. We define the stability requirement for feasible fixed points. We demonstrate algebraically that if the bifurcation (control) parameter rises over its threshold value, the system encounters flip and Neimark–Sacker (NS) bifurcations in the vicinity of the interior fixed point. We explicitly establish the existence requirements and direction of bifurcations via the center manifold theory. Analytical findings are validated by numerical simulations, which are used to highlight the occurrence of instability and chaotic dynamics in the system. In order to regulate the chaotic trajectories that exist in the system, we adopt a feedback control approach. |
| first_indexed | 2024-04-10T05:28:26Z |
| format | Article |
| id | doaj.art-d739028d97b442e7b676e4c44bbe6a8b |
| institution | Directory Open Access Journal |
| issn | 1607-887X |
| language | English |
| last_indexed | 2024-04-10T05:28:26Z |
| publishDate | 2023-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj.art-d739028d97b442e7b676e4c44bbe6a8b2023-03-07T11:58:35ZengHindawi LimitedDiscrete Dynamics in Nature and Society1607-887X2023-01-01202310.1155/2023/4555469Dynamical Complexities of a Discrete Ivlev-Type Predator-Prey SystemSarker Md. Sohel Rana0Department of MathematicsIn this study, we examine a discrete predator-prey system from the following two perspectives: (i) the functional response is of the Ivlev type and (ii) the prey growth rate is of the Gompertz type. We define the stability requirement for feasible fixed points. We demonstrate algebraically that if the bifurcation (control) parameter rises over its threshold value, the system encounters flip and Neimark–Sacker (NS) bifurcations in the vicinity of the interior fixed point. We explicitly establish the existence requirements and direction of bifurcations via the center manifold theory. Analytical findings are validated by numerical simulations, which are used to highlight the occurrence of instability and chaotic dynamics in the system. In order to regulate the chaotic trajectories that exist in the system, we adopt a feedback control approach.http://dx.doi.org/10.1155/2023/4555469 |
| spellingShingle | Sarker Md. Sohel Rana Dynamical Complexities of a Discrete Ivlev-Type Predator-Prey System Discrete Dynamics in Nature and Society |
| title | Dynamical Complexities of a Discrete Ivlev-Type Predator-Prey System |
| title_full | Dynamical Complexities of a Discrete Ivlev-Type Predator-Prey System |
| title_fullStr | Dynamical Complexities of a Discrete Ivlev-Type Predator-Prey System |
| title_full_unstemmed | Dynamical Complexities of a Discrete Ivlev-Type Predator-Prey System |
| title_short | Dynamical Complexities of a Discrete Ivlev-Type Predator-Prey System |
| title_sort | dynamical complexities of a discrete ivlev type predator prey system |
| url | http://dx.doi.org/10.1155/2023/4555469 |
| work_keys_str_mv | AT sarkermdsohelrana dynamicalcomplexitiesofadiscreteivlevtypepredatorpreysystem |