| 聂华,吴建华,谢文昊.一类具有抑制剂的非均匀恒化器模型的共存态[J].数学年刊A辑,2009,30(6):845~856 |
| 一类具有抑制剂的非均匀恒化器模型的共存态 |
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| Received:July 24, 2008 Revised:April 16, 2009 |
| DOI： |
| 中文关键词: 恒化器, Beddington-DeAngelis功能反应项, 共存解, 稳定性, 扰动理论 |
| 英文关键词:Chemostat, Beddington-DeAngelis functional response, Coexistence solution, Stability, Perturbation theory |
| 基金项目: |
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| 中文摘要: |
| 研究了一类具有抑制剂和Beddington-DeAngelis功能反应项的非均匀恒化器模型. 根据单调动力系统理论得到了正平衡解的存在性.
利用度理论、分歧理论以及摄动理论,分析了抑制剂对系统正平衡解及渐近行为的影响. 结果表明当体现抑制作用的参数μ充分大时, 此模型或者没有正解, 并且一个半平凡的非负解是全局吸引的; 或者模型的所有正解均由一个极限问题决定. |
| 英文摘要: |
| An unstirred chemostat model with inhibitor and Beddington-DeAngelis functional response is discussed. The existence of positive steady-state solutions is given by monotone system theory. The effects of the inhibitor are considered by making use of the degree theory, bifurcation theory and perturbation technique. It turns out that if the parameter μ, which measures the effect of the inhibitor, is sufficiently large, either this model has no coexistence solution and a semitrivial global attractor, or all positive solutions of this model are governed by a limit problem. |
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