| 一类分数阶比率依赖型捕食系统的动力学分析 |
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| 引用本文： | 蒲武军,杜争光.一类分数阶比率依赖型捕食系统的动力学分析[J].井冈山大学学报（自然科学版）,2021,42(2):14-18. |
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| 作者姓名： | 蒲武军 杜争光 |
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| 作者单位： | 陇南师范高等专科学校数学系, 甘肃, 陇南 742500,陇南师范高等专科学校数学系, 甘肃, 陇南 742500 |
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| 基金项目： | 陇南市2019年科技指导性计划项目（2019-ZD-14） |
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| 摘 要： | 讨论了一类食饵带有疾病的分数阶比率依赖型捕食系统的动力学行为。利用线性化方法定性分析了各类平衡点的稳定性,并给出了其正平衡点局部渐近稳定的充分条件。数值模拟显示,参数和阶数对平衡点的收敛速度及其稳定性产生很重要的影响。
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| 关 键 词： | 分数阶 比率依赖型捕食系统 局部渐近稳定性 Hopf分支 |
| 收稿时间： | 2020/10/14 0:00:00 |
| 修稿时间： | 2020/12/4 0:00:00 |
DYNAMICS OF A RATIO-DEPENDENT PREDATOR-PREY OF FRACTIONAL ORDER SYSTEM |
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| PU Wu-jun and DU Zheng-guang.DYNAMICS OF A RATIO-DEPENDENT PREDATOR-PREY OF FRACTIONAL ORDER SYSTEM[J].Journal of Jinggangshan University(Natural Sciences Edition),2021,42(2):14-18. |
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| Authors: | PU Wu-jun and DU Zheng-guang |
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| Institution: | Department of Mathematics, Longnan Teachers College, Longnan, Gansu 742500, China and Department of Mathematics, Longnan Teachers College, Longnan, Gansu 742500, China |
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| Abstract: | In this paper, we studied the dynamic behavior of a fractional-order ratio-dependent predator-prey system with disease on the prey. The stability of all kinds of equilibrium points of the system was qualitatively analyzed with the linearization method, the sufficient conditions for the local asymptotic stability of the positive equilibrium point of the system were given, and the numerical simulation showed that the parameters and order of the system had an important influence on the convergence rate and stability of the equilibrium point. |
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| Keywords: | fractional-order ratio-dependent predator-prey model local asymptotic stability Hopf bifurcation |
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