| 庞丹凤,聂 华,臧 辉.一类具有抑制剂和质载的非均匀恒化器模型的共存解[J].数学年刊A辑,2016,37(2):171~190 |
| 一类具有抑制剂和质载的非均匀恒化器模型的共存解 |
| Coexistence Solutions of the Unstirred Chemostat Modelwith Inhibitor and Plasmid |
| Received:April 18, 2014 Revised:June 13, 2015 |
| DOI： |
| 中文关键词: 恒化器, 抑制剂, 不动点指标理论, 摄动理论, 稳定性 |
| 英文关键词:Chemostat, Inhibitor, Fixed point index theory, Perturbation theory, Stability |
| 基金项目: |
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| 中文摘要: |
| 研究了一类具有抑制剂和质载的非均匀恒化器模型.
首先, 采用锥映射上不动点指标理论得到了物种共存的充分条件.
然后, 根据度理论及摄动理论, 研究了模型正平衡态解的唯一性和稳定性.
结果表明当抑制剂的影响充分大时, 模型存在唯一的渐近稳定的共存解.
最后, 利用比较原理和一致持续理论研究了系统的长时行为, 并采用数值模拟的方法对所得
结论进行了验证和补充. |
| 英文摘要: |
| First, sufficient conditions of coexistence are determined by the fixed point index theory in cone.
Second, the uniqueness and stability of positive steady state solution are investigated by the degree theory and perturbation technique.
It turns out that if the effects of the inhibitor are sufficiently large, then this model has only one asymptotically stable coexistence solution.
Finally, the long-time behavior of the system is studied by the comparison principle and uniform persistence theory.
Numerical simulations are applied to verify and supplement the analytic outcomes. |
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