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Local Bifurcations in a Nonlinear Model of a Bioreactor

Dimitrova, Neli — 2009

Serdica Journal of Computing

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...

One-Parameter Bifurcation Analysis of Dynamical Systems using Maple

Borisov, MilenDimitrova, Neli — 2010

Serdica Journal of Computing

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.

Global Asymptotic Stability of a Functional Differential Model with Time Delay of an Anaerobic Biodegradation Process

Borisov, MilenDimitrova, NeliKrastanov, Mikhail — 2017

Serdica Journal of Computing

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...

Nonlinear stabilizing control of an uncertain bioprocess model

Neli DimitrovaMikhail Krastanov — 2009

International Journal of Applied Mathematics and Computer Science

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...

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