Stability and Bifurcation Analysis of a Discrete Singular Bioeconomic System
The main concern of this paper is to discuss stability and bifurcation analysis for a class of discrete predator-prey interaction with Holling type II functional response and harvesting effort. Firstly, we establish a discrete singular bioeconomic system, which is based on the discretization of a sy...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2021/6679161 |
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| author | Qamar Din A. M. Yousef A. A. Elsadany |
| author_facet | Qamar Din A. M. Yousef A. A. Elsadany |
| author_sort | Qamar Din |
| collection | DOAJ |
| description | The main concern of this paper is to discuss stability and bifurcation analysis for a class of discrete predator-prey interaction with Holling type II functional response and harvesting effort. Firstly, we establish a discrete singular bioeconomic system, which is based on the discretization of a system of differential algebraic equations. It is shown that the discretized system exhibits much richer dynamical behaviors than its corresponding continuous counterpart. Our investigation reveals that, in the discretized system, two types of bifurcations (i.e., period-doubling and Neimark–Sacker bifurcations) can be studied; however, the dynamics of the continuous model includes only Hopf bifurcation. Moreover, the state delayed feedback control method is implemented for controlling the chaotic behavior of the bioeconomic model. Numerical simulations are presented to illustrate the theoretical analysis. The maximal Lyapunov exponents (MLE) are computed numerically to ensure further dynamical behaviors and complexity of the model. |
| format | Article |
| id | doaj-art-d6c0fc31bd024743a255e01fe0e99487 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-d6c0fc31bd024743a255e01fe0e994872025-02-03T01:27:09ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2021-01-01202110.1155/2021/66791616679161Stability and Bifurcation Analysis of a Discrete Singular Bioeconomic SystemQamar Din0A. M. Yousef1A. A. Elsadany2Department of Mathematics, University of Poonch Rawalakot, Rawalakot 12350, PakistanMathematics Department, Faculty of Science, South Valley University, Qena, EgyptMathematics Department, College of Science and Humanities Studies in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi ArabiaThe main concern of this paper is to discuss stability and bifurcation analysis for a class of discrete predator-prey interaction with Holling type II functional response and harvesting effort. Firstly, we establish a discrete singular bioeconomic system, which is based on the discretization of a system of differential algebraic equations. It is shown that the discretized system exhibits much richer dynamical behaviors than its corresponding continuous counterpart. Our investigation reveals that, in the discretized system, two types of bifurcations (i.e., period-doubling and Neimark–Sacker bifurcations) can be studied; however, the dynamics of the continuous model includes only Hopf bifurcation. Moreover, the state delayed feedback control method is implemented for controlling the chaotic behavior of the bioeconomic model. Numerical simulations are presented to illustrate the theoretical analysis. The maximal Lyapunov exponents (MLE) are computed numerically to ensure further dynamical behaviors and complexity of the model.http://dx.doi.org/10.1155/2021/6679161 |
| spellingShingle | Qamar Din A. M. Yousef A. A. Elsadany Stability and Bifurcation Analysis of a Discrete Singular Bioeconomic System Discrete Dynamics in Nature and Society |
| title | Stability and Bifurcation Analysis of a Discrete Singular Bioeconomic System |
| title_full | Stability and Bifurcation Analysis of a Discrete Singular Bioeconomic System |
| title_fullStr | Stability and Bifurcation Analysis of a Discrete Singular Bioeconomic System |
| title_full_unstemmed | Stability and Bifurcation Analysis of a Discrete Singular Bioeconomic System |
| title_short | Stability and Bifurcation Analysis of a Discrete Singular Bioeconomic System |
| title_sort | stability and bifurcation analysis of a discrete singular bioeconomic system |
| url | http://dx.doi.org/10.1155/2021/6679161 |
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