Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability of the chemostat system with a mutation factor   In this paper, we consider a resource-consumer model taking into account a
mutation effect between species (with constant mutation rate). The
corresponding mutation operator is a discretization of the Laplacian in such a
way that the resulting dynamical system can be viewed as a regular perturbation
of the classical chemostat system. We prove the existence of a unique locally
stable steady-state for every value of the mutation rate and every value of the
dilution rate not exceeding a critical value. In addition, we give an expansion
of the steady-state in terms of the mutation rate and we prove a uniform
persistence property of the dynamics related to each species. Finally, we show
that this equilibrium is globally asymptotically stable for every value of the
mutation rate provided that the dilution rate is with small enough values.

13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph