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Discretization of a fractional order ratio-dependent functional response predator-prey model, bifurcation and chaos | ||
| Computational Methods for Differential Equations | ||
| مقاله 9، دوره 6، شماره 2، تیر 2018، صفحه 248-265 اصل مقاله (4.87 M) | ||
| نوع مقاله: Research Paper | ||
| نویسندگان | ||
| Razie Shafeii Lashkarian* 1؛ Dariush Behmardi Sharifabad2 | ||
| 1Department of Basic science, Hashtgerd Branch, Islamic Azad University, Alborz, Iran | ||
| 2Department of Mathematics, Alzahra university, Tehran, Iran | ||
| چکیده | ||
| This paper deals with a ratio-dependent functional response predator-prey model with a fractional order derivative. The ratio-dependent models are very interesting, since they expose neither the paradox of enrichment nor the biological control paradox. We study the local stability of equilibria of the original system and its discretized counterpart. We show that the discretized system, which is not more of fractional order, exhibits much richer dynamical behavior than its corresponding fractional order model. Specially, in the discretized system, many types of bifurcations (transcritical, flip, Neimark-Sacker) and chaos may happen, however, the local analysis of the fractional-order counterpart, only deals with the stability (unstability) of the equilibria. Finally, some numerical simulations are performed by MATLAB, to support our analytic results. | ||
| کلیدواژهها | ||
| Ratio-dependent functional response model؛ Fractional derivative؛ Discretization؛ Bifurcation؛ chaos | ||
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آمار تعداد مشاهده مقاله: 825 تعداد دریافت فایل اصل مقاله: 993 |
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