Coexistence of an unstirred chemostat model with B-D functional response by fixed point index theory

Bifurcation and Stability for the Unstirred Chemostat Model with Beddington-deangelis Functional

Abstract. In this paper, we consider a basic N-dimensional competition model in the unstirred chemostat with Beddington-DeAngelis functional response. The bifurcation solutions from a simple eigenvalue and a double eigenvalue are obtained respectively. In particular, for the double eigenvalue, we establish the existence and stability of coexistence solutions by the techniques of space decomposi...

Competition in the Unstirred Chemostat with Periodic Input and Washout

The Lefschetz Principle , Fixed Point Theory , and Index Theory

This is a rough historical account of some uses of the Lefschetz Principle in fixed point theory and index theory. The Lefschetz Principle states that the alternating sum of the traces on cohomology (a global and rigid invariant) is equal to the alternating sum of the traces on the underlying cochain complex (a local and far less rigid invariant). The original Lefschetz Theorem for compact poly...

A Topological Fixed-Point Index Theory for Evolution Inclusions

In the paper we construct a topological fixed-point theory for a class of set-valued maps which appears in natural way in boundary value problems for differential inclusions. Our construction is based upon the notion of (U, V )-approximation in the sense of Ben-El-Mechaiekh and Deguire. As applications we consider initial-value problems for nonlinear evolution inclusions of the type x′(t) ∈ −A(...

Further studies of a reaction-diffusion system for an unstirred chemostat with internal storage

The dynamics of a reaction-diffusion system for two species of microorganism in an unstirred chemostat with internal storage is studied. It is shown that the diffusion coefficient is a key parameter of determining the asymptotic dynamics, and there exists a threshold diffusion coefficient above which both species become extinct. On the other hand, for diffusion coefficient below the threshold, ...