| 具有Beddington-DeAngelis功能反应项的捕食-食饵扩散模型的稳定性 |
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| 引用本文： | 付娟,张睿,王彩军,张婧.具有Beddington-DeAngelis功能反应项的捕食-食饵扩散模型的稳定性[J].山东大学学报(理学版),2016,51(11):115-122. |
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| 作者姓名： | 付娟 张睿 王彩军 张婧 |
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| 作者单位： | 兰州交通大学数理学院, 甘肃 兰州 730070 |
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| 基金项目： | 国家自然科学基金资助项目(11561041,61563026) |
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| 摘 要： | 考虑了一类带有扩散的Beddington-DeAngelis捕食者-食饵模型。 通过线性化方法和构造Lyapunov函数得到弱耦合反应扩散系统非负平衡点的局部和全局渐近稳定性; 分析了交错扩散系统对非负平衡点稳定性的影响, 并且得到了交错扩散导致Turing不稳定的区域。
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| 关 键 词： | 自扩散 交错扩散 稳定性 Lyapunov函数 捕食者-食饵模型 |
| 收稿时间： | 2016-06-17 |
The stability of a predator-prey diffusion model with Beddington-DeAngelis functional response |
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| FU Juan,ZHANG Rui,WANG Cai-jun,ZHANG Jing.The stability of a predator-prey diffusion model with Beddington-DeAngelis functional response[J].Journal of Shandong University,2016,51(11):115-122. |
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| Authors: | FU Juan ZHANG Rui WANG Cai-jun ZHANG Jing |
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| Affiliation: | Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China |
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| Abstract: | We consider a diffusive predator-prey model with Beddington-DeAngelis functional response. First, the local and global asymptotic stabilities of the nonnegative equilibrium point of weakly coupled reaction-diffusion system are obtained by linearization and constructing Lyapunov function. Secondly, the effect of cross-diffusion coefficient on the stability of the nonnegative equilibrium point is discussed. The results show that cross-diffusion can induce Turing unstable region. |
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| Keywords: | self-diffusion stability cross-diffusion lyapunov function predator-prey model |
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