Bifurcation analysis of a model of plasmid-bearing, plasmid-free competition in a pulsed chemostat with an internal inhibitor
Bifurcation analysis of a model of plasmid-bearing, plasmid-free competition in a pulsed chemostat with an internal inhibitor
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具有内部抑制剂的脉冲恒化器中携带质粒、无质粒竞争的模型的分叉分析
DOI：
10.1093/imamat/hxq036
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发表时间：
2011-04
期刊：
影响因子：
--
通讯作者：
Zhang, Weiguo
中科院分区：
文献类型：
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作者：
Zhao, Yu;Yuan, Sanling;Zhang, Weiguo
本文研究了脉冲恒化器中携带质粒和不携带质粒的生物之间的竞争模型。假定携带质粒的生物体将其资源的一部分用于向不携带质粒的生物体产生毒素。我们研究了不含质粒生物的子系统，并研究了周期解的稳定性，这是系统的边界周期解。边界周期解的稳定性分析得到了携带质粒生物的入侵阈值。通过使用分岔理论的标准技术，我们证明了在这个阈值以上，营养、无质粒和携带质粒的生物和抑制剂存在周期性振荡。数值模拟验证了本文的研究结果。
A model of competition between plasmid-bearing and plasmid-free organisms in a pulsed chemostat is considered in this paper. It is assumed that the plasmid-bearing organism devotes a portion of its resources to producing a toxin to the plasmid-free organism. We investigate the subsystem in the absence of plasmid-bearing organism and study the stability of the periodic solutions, which are the boundary periodic solutions of the system. The stability analysis of the boundary periodic solution yields the invasion threshold of the plasmid-bearing organism. By use of standard techniques of bifurcation theory, we prove that above this threshold there are periodic oscillations in nutrient, plasmid-free and plasmid-bearingorganisms and inhibitor. Numerical simulations are carried out to illustrate our results.