Analysis of competitive chemostat models with the Beddington–DeAngelis functional response and impulsive effect |
| |
Authors: | Xueyong Zhou Xinyu Song Xiangyun Shi |
| |
Institution: | Department of Mathematics, Xinyang Normal University, Xinyang 464000, Henan, PR China |
| |
Abstract: | In this paper, we introduce and study a competitive system with Beddington–DeAngelis type functional response in periodic pulsed chemostat conditions. We investigate the subsystem with substrate and one of the microorganisms and study the stability of the periodic solutions, which are the boundary periodic solution of the system. The stability analysis of the boundary periodic solution yields an invasion threshold. By use of standard techniques of bifurcation theory, we prove that above this threshold there are periodic oscillations in substrate and one of the microorganism. Further, we prove that the system is permanent if the impulsive period less than some critical value. Therefore, our results are valuable for the manufacture of products by genetically altered organisms. |
| |
Keywords: | 34C05 92D25 |
本文献已被 ScienceDirect 等数据库收录! |
|