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This paper deals with the problem of feedback control of competition between two species with one substrate in the chemostat with nonmonotone growth functions. Without control, the generic behavior is competitive exclusion. The aim of this paper is to find a feedback control of the dilution rate, depending only on the total biomass, such that coexistence… (More)
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.… (More)
We prove that the well-known 3/2 stability condition established for the Wright equation (WE) still holds if the nonlinearity p(exp(−x)−1) in WE is replaced by a decreasing or unimodal smooth function f with f ′ (0) < 0 satisfying the standard negative feedback and below boundedness conditions and having everywhere negative Schwarz derivative.
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… (More)
We present a model of single species fishery which alternates closed seasons with pulse captures. The novelty is that the length of a closed season is determined by the remaining stock size after the last capture. The process is described by a new type of impulsive differential equations recently introduced. The main result is a fishing effort threshold… (More)