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Dynamics and bifurcation control of a fractional-order delayed predator–prey model with an omnivore | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 16 مهر 1403 اصل مقاله (1.8 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2024.61871.2696 | ||
| نویسندگان | ||
| Abdul Hussain Surosh1؛ Reza Khoshsiar Ghaziani* 2؛ Javad Alidoosti2 | ||
| 1Department of Mathematics, Baghlan University, Pol-e-Khomri, Baghlan, Afghanistan. | ||
| 2Department of Applied Mathematics, Shahrekord University, Shahrekord, P.O. Box 115, Iran. | ||
| چکیده | ||
| In this study, we propose a novel fractional delayed predator-prey model that includes an omnivorous species and explore bifurcation control through a state feedback control strategy. We begin by deriving the characteristic polynomial using the Laplace transform and establish new sufficient conditions for stability analysis and Hopf bifurcation, treating the time delay $ \tau $ as a bifurcation parameter. To address Hopf bifurcation in the uncontrolled system, we design a state feedback controller with time delay. Our results indicate that the time delay $ \tau $ significantly affects the onset of Hopf bifurcation. Additionally, the inclusion of fractional order $ 0<\alpha \leq 1 $ enhances solution stability while adding complexity to dynamics of the model. We find that judicious selection of the feedback gain can delay bifurcation, highlighting the critical role of control effort. To validate our theoretical findings, we present numerical simulations conducted using a modified Adams-Bashforth-Moulton predictor-corrector method. These simulations support our theoretical results and demonstrate the efficacy of our proposed control strategy in managing dynamical behaviors of the model. | ||
| کلیدواژه‌ها | ||
| Fractional order؛ Bifurcation control؛ Predator–prey model؛ Time–delay؛ Hopf bifurcation | ||
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آمار تعداد مشاهده مقاله: 124 تعداد دریافت فایل اصل مقاله: 127 |
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