| 窦晓霞,李海侠.比率依赖的修正Leslie-Gower捕食-食饵模型正解存在性和唯一性[J].,2022,62(2):213-220 |
| 比率依赖的修正Leslie-Gower捕食-食饵模型正解存在性和唯一性 |
| Existence and uniqueness of positive solutions for ratio-dependent modified Leslie-Gower predator-prey model |
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| DOI：10.7511/dllgxb202202014 |
| 中文关键词: 捕食-食饵模型 不动点指数理论 扰动理论 唯一性 稳定性 渐近行为 |
| 英文关键词: predator-prey model fixed point index theory perturbation theory uniqueness stability asymptotic behavior |
| 基金项目:国家自然科学基金资助项目(6167202111801013)；陕西省自然科学基础研究计划项目(2014JQ21003)；宝鸡市科技计划项目(2018JH20)；宝鸡文理学院校级重点项目(ZK2546). |
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| 中文摘要: |
| 研究了一类基于比率依赖的修正Leslie-Gower捕食-食饵扩散模型．首先利用不动点指数理论给出了正解的存在条件．其次通过扰动理论结合不动点指数理论讨论了正解的唯一性和稳定性，得到了正解唯一且稳定的条件．最后运用抛物方程的比较原理分析了系统的渐近行为．研究结果表明，参数满足一定条件时，两物种能够共存，而且系统恰好存在唯一稳定的正解． |
| 英文摘要: |
| A ratio-dependent modified Leslie-Gower predator-prey model with diffusion is investigated. By the fixed point index theory, the condition for the existence of positive solutions is given. Secondly, the uniqueness and stability of positive solutions are studied by means of the combination of the perturbation theory and the fixed point index theory, and the condition of the uniqueness and stability of positive solutions is determined. Finally, by virtue of the comparison principle to parabolic equations, the asymptotic behavior of the system is discussed. The results show that if the parameters meet certain conditions, the two species can coexist and the system has unique stable positive solution. |
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