Global analysis of a delayed Monod type chemostat model with impulsive input on two substrates

Advances in Difference Equations

Peiguang Wang¹  Jianzhi Cao²  Junyan Bao² 

[1] College of Electronic and Information Engineering, Hebei University, Baoding, P.R. China;College of Mathematics and Information Science, Hebei University, Baoding, P.R. China

关键词: Monod type;    globally attractivity;    nutrient recycling;    chemostat model;    34K45;    34K20;   

DOI  :  10.1186/s13662-015-0623-3

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, a new Monod type chemostat model with delay and impulsive input on two substrates is considered. By using the global attractivity of a k times periodically pulsed input chemostat model, we obtain the bound of the system. By the means of a fixed point in a Poincaré map for the discrete dynamical system, we obtain a semi-trivial periodic solution; further, we establish the sufficient conditions for the global attractivity of the semi-trivial periodic solution. Using the theory on delay functional and impulsive differential equations, we obtain a sufficient condition with time delay for the permanence of the system.

【 授权许可】

CC BY