In this paper we consider a nonlinear model of a biological wastewater treatment process, based on two microbial populations and two substrates. The model, described by a four-dimensional dynamic system, is known to be practically verified and reliable. First we study the equilibrium points of the open-loop system, their stability and local bifurcations with respect to the control variable. Further we propose a feedback control law for asymptotic stabilization of the closed-loop system towards a...
This paper is partially supported by the Bulgarian Science Fund under grant Nr. DO 02–
359/2008.
We consider a nonlinear model of a continuously stirred bioreactor
and study the stability of the equilibrium points with respect to practically
important model parameters. We determine regions in the parameter
space where the steady states undergo transcritical and Hopf bifurcations.
In the latter case, the stability of the emerged limit cycles is also studied.
Numerical simulations in the...
This paper presents two algorithms for one-parameter local
bifurcations of equilibrium points of dynamical systems.
The algorithms are implemented in the computer algebra system Maple 13 © and designed as a package. Some examples are reported to demonstrate the package’s facilities.
* This paper is partially supported by the Bulgarian Science Fund under grant Nr. DO 02–359/2008.
We study a nonlinear functional differential model of an anaerobic
digestion process of wastewater treatment with biogas production. The
model equations of biomass include two different discrete time delays. A
mathematical analysis of the model is completed including existence and
local stability of nontrivial equilibrium points, existence and boundedness
of the model solutions as well as global stabilizability towards an admissible
equilibrium point. We propose and apply a numerical extremum seeking
algorithm...
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