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一类捕食-食饵模型正解的存在性

Existence of Positive Solutions for a Predator-prey Model
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摘要 研究了一类捕食-食饵模型,其中捕食者的密度干扰项的系数与食饵密度有关。首先,利用Leray-Schauder度理论,通过计算不动点的指数,结合特征值的比较原理得出了正平衡解存在的充分条件;然后,利用Turing理论,讨论了该模型半平凡解的稳定性情况;最后讨论了解的渐近行为,运用半动力系统的一致持续理论给出了正解一致持续的充分条件。 The predator-prey model whose predator＇s density interference term＇s coefficient is related with prey is investigated. First, by calculating the index of the fixed point, some sufficient conditions for the existence of pos- itive steady-state solutions are obtained. Furthermore, the stability of the semi-trivial solutions is discussed by Tur- ing theory. Finally, the asymptotic behavior of solutions is discussed, and by applying permanence theory in semi- dynamical systems sufficient conditions for the permanence of this system are derived.
作者 张凡 李艳玲
机构地区 陕西师范大学数学与信息科学学院
出处 《科学技术与工程》 2010年第19期4597-4603,共7页 Science Technology and Engineering
基金 国家自然科学基金(10971124) 教育部高等学校博士点专项基金(200807180004)资助
关键词 平衡解 不动点指数 稳定性 一致持续 steady-state solution index of fixed point stability uniform permanence
分类号 O175.26 [理学—基础数学]
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参考文献11

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二级参考文献7

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科学技术与工程
2010年 第19期

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