Characterization of positive solutions of the unstirred chemostat with an inhibitor

Nie H; Zhang HW; Wu HH

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Characterization of positive solutions of the unstirred chemostat with an inhibitor

机译：用抑制剂表征未搅拌的恒化器的正溶液

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This paper deals with the unstirred chemostat model in the presence of an internal inhibitor. The main purpose of the paper is to determine the exact range A of the maximal growth (a, h) of two species where the system possesses positive solutions. It turns out that Lambda is a connected unbounded region in R-+(2), whose boundary consists of two monotone nondecreasing curves Gamma(1) : a = H-1 (b) and Gamma(2) : b = H-2 (a). For every (a, b) inside Lambda the system has positive solutions and for (a, b) outside Lambda there exists no positive solution. The functions H-1 (b) and H2 (a) are constructed in terms of the limit of the corresponding time-dependent solution with a specific initial function. In particular, it is also shown that the system has at least two positive solutions in certain subregion of Lambda. (C) 2007 Elsevier Ltd. All rights reserved.

机译：本文研究了在内部抑制剂存在下的非搅拌式恒化器模型。本文的主要目的是确定系统具有正解的两个物种的最大生长（a，h）的确切范围A。事实证明Lambda是R-+（2）中的一个连通无界区域，其边界由两条单调非递减曲线Gamma（1）：a = H-1（b）和Gamma（2）：b = H-2组成（一种）。对于Lambda内部的每个（a，b）系统都有正解，而Lambda外部的（a，b）没有正解。函数H-1（b）和H2（a）是根据具有特定初始函数的时间相关解的极限构造的。特别地，还示出了该系统在Lambda的某些子区域中具有至少两个正解。（C）2007 Elsevier Ltd.保留所有权利。

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《Nonlinear analysis. Real world applications》 |2008年第3期|共12页
作者
Nie H; Zhang HW; Wu HH;
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正文语种 eng
中图分类数学分析;
关键词
chemostat; fixed point index; monotone method; REACTION-DIFFUSION EQUATIONS; 2 COMPETITORS; SYSTEM; MODEL; COEXISTENCE; BIFURCATION; RESOURCES; BACTERIA; STATE;

机译：恒化器;不动点指数;单调法;反应扩散方程;2个竞争者;系统;模型;共存;分叉;资源;细菌;状态;

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1. Characterization of positive solutions of the unstirred chemostat with an inhibitor [J] . Nie H, Zhang HW, Wu HH Nonlinear analysis. Real world applications . 2008,第3期

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Characterization of positive solutions of the unstirred chemostat with an inhibitor

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