A study on a Ivlev-type Chemostat model with one competitor producing a toxin

2017 International Symposium on Application of Materials Science and Energy Materials

材料科学;能源学

Sun, Mingjuan^1

School of Mathematics and Computer Science, Yanan University, Yanan, China^1

关键词: Chemostat models;    Functional response;    Globally asymptotically stable;    LaSalle invariant principle;    Local asymptotic stability;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/322/5/052014/pdf
DOI  :  10.1088/1757-899X/322/5/052014

学科分类：材料科学（综合）

来源: IOP

【 摘 要 】

In order to illustrate the phenomena microorganisms produce toxins to compete with its competitors, a Chemostat model of two competitors for single nutrient with Ivlev-type functional response is investigated. The existence of its solutions is analysed, and the local asymptotic stability of the model's equilibria is obtained. By use of the theory of limit systems and Lyapunov-LaSalle invariant principle, it is shown that its equilibria are globally asymptotically stable under some conditions. Our results demonstrate that the principle of competition exclusion is established, and under different conditions, different microorganism can beat the competition.