Abstract
In this paper, the author investigates Chemostat with Delay and Simplifified Holling Type-IV Response Function, which more match the actual meaning in the chemostat system. Using bifurcation theory, we discuss the hopf bifurcation stability in detail.
Highlights
Chemostat is a amplified model of lakes, it has great significance in biology
This paper considers a simplified Holling IV type (6) system, s s0 x, t
There is a concern of internal equilibrium, the direction of HOPF bifurcation and the stability of the nearby
Summary
Chemostat is a amplified model of lakes, it has great significance in biology. On the Chemostat model of various types of equations, such as ordinary deferential equation, partial deferential equations and delay deferential equations. There are a lot of results about the p(s) is a type of Holling II functional response. Considering the highly concentration medium on inhibition of microbial growth, Andrews[4] proposed Holling IV type functional response function which was non monotonic in 1968, p(s) ms a bs s2. Sokol and Howell proposed Holling IV type functional response function is simplified (see [5]). This function (6) is similar to function (5), and can better fit the experimental data (see [4], [6]), which contains only two parameters m and a, so the (5) is more widely used. This paper considers a simplified Holling IV type (6) system, s s0s, x s0 x , t t ,a D s0a, m mD, D t [ ,0] ,
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