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Mathematical Problems in Engineering
Volume 2013, Article ID 685452, 8 pages
http://dx.doi.org/10.1155/2013/685452
Research Article

Dynamics of a Bioreactor with a Bacteria Piecewise-Linear Growth Model in a Methane-Producing Process

1Departamento de Matemáticas y Estadística, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Colombia-Sede Manizales, Carrera 27 No. 64-60 Manizales, Caldas, Colombia
2Departamento de Ingeniería Eléctrica, Electrónica y Computación, Percepción y Control Inteligente-Bloque Q, Facultad de Ingeniería y Arquitectura, Universidad Nacional de Colombia-Sede Manizales, Bloque Q, Campus La Nubia, Manizales 170003, Colombia

Received 13 December 2012; Revised 20 August 2013; Accepted 4 October 2013

Academic Editor: Bing Chen

Copyright © 2013 Luz A. Melo Varela et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper shows a study, both analytical and numerical, of a continuous-time dynamical system associated with a simple model of a wastewater biorreactor. Nonsmooth phenomena and border-collision local bifurcations appear when the main parameters (dilution and biomass concentration at the inflow) are varied. We apply the Filippov methods following Kuznetsov’s work.