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一类捕食-食饵模型共存解的存在性与稳定性 被引量:10

Coexistence of existence and stability of a predator-prey model
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摘要 研究了一类具有HollingⅢ型捕食-食饵模型平衡态正解的存在性与稳定性.利用锥上的不动点理论给出正解存在的充分条件;讨论了m充分大时,借助上下解方法构造出模型的正解,并根据线性稳定性理论讨论了该正解的稳定性.结果表明:当参数a>λ1,c>λ1(-dθ2a/(1+mθ2a))时,共存解存在,且当c>λ1时,共存解是线性稳定的. Abstract: The existence and stability of positive solutions are investigated for a predator-prey model with Holling type [[[ functional response. By using the fixed point index in cones, one can reduce the sufficient conditions for any possible positive solutions. When m is suitably large,by the super-sub solution method for predator-prey systems, the positive solutions and the stability of the positive solutions are studied by using the linearized stability. It is shown that the models a〉λ1,c〉λ1(-dθ2α/1+mθ2α)md the coexistence solution is linear sta-bility if c〉λ1
出处 《陕西师范大学学报(自然科学版)》 CAS CSCD 北大核心 2014年第1期15-18,共4页 Journal of Shaanxi Normal University:Natural Science Edition
基金 国家自然科学基金资助项目(11271236) 教育部高等学校博士学科点专项科研基金项目(200807180004)
关键词 捕食-食饵模型 稳定性 不动点指数 predator-prey model~ stability~ fixed point index
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参考文献6

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共引文献1

同被引文献54

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