Global Periodic Solution Of The Chemostat With Delay And Simplified Holling Type-Ⅳ Response Function

In this paper,we adopt the Holling IV Functional Response,namely p(s) = ms/(a + s~2), which more match the actual meaning in the chemostat to the follow equation:study the existence of nonconstant periodic solutions , and analysis the Hopf bifurcation in detail.This paper is composed of three sections. In section 1, we introduce the production and development of the chemostat, the system which will be discussed and the chief work of this paper. We also explain why the simplified Holling type-IV response function can be used in this system.In section 2, we analysis the bifurcation direction and stability of the system by making use of the related knowledge of the bifurcation and passing the detailed calculation.In section 3, we construct the special function and analysis the functional graph, we study the global periodic solution with only one interior stable point by ejective fixed point theory.