We propose a model of competition of n species in a chemostat, with constant input of
some species. We mainly emphasize the case that can lead to coexistence in the chemostat
in a non-trivial way, i.e., where the n−1 less competitive species are in the input. We prove
that if the inputs satisfy a constraint, the coexistence between the species is obtained in the
form of a globally asymptotically stable (GAS) positive equilibrium, while a GAS equilibrium
without the dominant species is achieved if the constraint is not satisfied. This work is
round up with a thorough study of all the situations that can arise when having an arbitrary
number of species in the chemostat inputs; this always results in a GAS equilibrium that
either does or does not encompass one of the species that is not present in the input
Abstract. In this paper we consider a control problem for an uncertain chemostat model with a general growth function and cell mortality. This uncertainty affects the model (growth function) as well as the outputs (measurements of substrate). Despite this lack of information, an upper bound and a lower bound for those uncertainties are assumed to be known a priori. We build a family of feedback control laws on the dilution rate, giving a guaranteed estimation on the unmeasured variable (biomass), and stabilizing the two variables in a rectangular set, around a reference value of the substrate. We give two realistic applications of this control law to a depollution process and to phytoplankton culture.
Artículo de publicación ISIWe study differentiability properties in a particular case of the Palmer's linearization theorem, which states the existence of a homeomorpbism H between the solutions of a linear ODE system having exponential dichotomy and a quasilinear system. Indeed, if the linear system is uniformly asymptotically stable, sufficient conditions ensuring that H is a C-2 preserving orientation diffeomorphism are given. As an application, we generalize a converse result of density functions for a nonlinear system in the nonautonomous case.FONDECYT Iniciacion Project
11121122
Center of Dynamical Systems and Related Fields DySyRF (Anillo Project, CONICYT)
1103
FONDECYT Regular Project
112070
We prove that, under some conditions, a linear nonautonomous difference system is Bylov's almost reducible to a diagonal one whose terms are contained in the Sacker and Sell spectrum of the original system.We also provide an example of the concept of diagonally significant system, recently introduced by Pötzche. This example plays an essential role in the demonstration of our results.
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