| 具有空间异质和合作捕食的捕食-食饵模型的正解 |
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| 引用本文： | 韩卓茹,李善兵.具有空间异质和合作捕食的捕食-食饵模型的正解[J].山东大学学报(理学版),2022,57(7):35-42. |
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| 作者姓名： | 韩卓茹 李善兵 |
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| 作者单位： | 西安电子科技大学数学与统计学院, 陕西 西安 710126 |
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| 基金项目： | 国家自然科学基金资助项目(11901446);中国博士后特别资助项目(2021T140530);西安市科协青年人才托举计划项目(095920201325) |
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| 摘 要： | 研究了一类具有空间异质和合作捕食的捕食-食饵模型的平衡态问题。首先利用Riesz-Schauder理论,得到了平凡解和半平凡解的局部渐近稳定性;其次利用比较原理,证明了平凡解和半平凡解的全局渐近稳定性;最后利用不动点指数理论,建立了正解存在的充分条件。
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| 关 键 词： | 捕食-食饵模型 空间异质 合作捕食 稳定性 正解 |
Positive solutions of predator-prey model with spatial heterogeneity and hunting cooperation |
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| HAN Zhuo-ru,LI Shan-bing.Positive solutions of predator-prey model with spatial heterogeneity and hunting cooperation[J].Journal of Shandong University,2022,57(7):35-42. |
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| Authors: | HAN Zhuo-ru LI Shan-bing |
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| Institution: | College of Mathematics and Statistics, Xidian University, Xian 710126, Shaanxi, China |
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| Abstract: | The steady-state problem of a predator-prey model with spatial heterogeneity and hunting cooperation is investigated. Firstly, by using the Riesz-Schauder theory, the local asymptotic stability of trivial solution and semi-trivial solutions is obtained. By means of the comparison principle, the global asymptotic stability of trivial solution and semi-trivial solutions is derived. Finally, the sufficient conditions for the existence of positive solutions are established by the fixed point index theory. |
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| Keywords: | predator-prey model spatial heterogeneity hunting cooperations positive solutions stability |
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