Skip to main content

Functional Differential Model of an Anaerobic Biodegradation Process

  • Conference paper
  • First Online:
Large-Scale Scientific Computing (LSSC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 9374))

Included in the following conference series:

  • 685 Accesses

Abstract

In this paper we study a nonlinear functional differential model of a biological digestion process, involving two microbial populations and two substrates. We establish the global asymptotic stability of the model solutions towards a previously chosen equilibrium point and in the presence of two different discrete delays. Numerical simulation results are also included.

This research has been partially supported by the Sofia University “St Kl. Ohridski” under contract No. 08/26.03.2015.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Alcaraz-González, V., Harmand, J., Rapaport, A., Steyer, J.-P., González-Alvarez, V., Pelayo-Ortiz, C.: Software sensors for highly uncertain WWTPs: a new apprach based on interval observers. Water Res. 36, 2515–2524 (2002)

    Article  Google Scholar 

  2. Bernard, O., Hadj-Sadok, Z., Dochain, D.: Advanced monitoring and control of anaerobic wastewater treatment plants: dynamic model develop- ment and identification. In: Proceedings of Fifth IWA International Sympposium WATERMATEX, Gent, Belgium, pp. 3.57-3.64 (2000)

    Google Scholar 

  3. Bernard, O., Hadj-Sadok, Z., Dochain, D., Genovesi, A., Steyer, J.-P.: Dynamical model development and parameter identification for an anaerobic wastewater treatment process. Biotechnol. Bioeng. 75, 424–438 (2001)

    Article  Google Scholar 

  4. Dimitrova, N.S., Krastanov, M.I.: On the asymptotic stabilization of an uncertain bioprocess model. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds.) LSSC 2011. LNCS, vol. 7116, pp. 115–122. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  5. Dimitrova, N.S., Krastanov, M.I.: Model-based optimization of biogas production in an anaerobic biodegradation process. Comput. Math. Appl. 68, 986–993 (2014)

    Article  MathSciNet  Google Scholar 

  6. Gopalsamy, K.: Stability and Oscillations in Delay Differential Equations of Population Dynamics. Kluwer Academic Publishers, Dordrect (1992)

    Book  MATH  Google Scholar 

  7. Grognard, F., Bernard, O.: Stability analysis of a wastewater treatment plant with saturated control. Water Sci. Technol. 53, 149–157 (2006)

    Article  Google Scholar 

  8. Hale, J.K.: Theory of Functional Differential Equations. Applied Mathematical Sciences, vol. 3. Springer, New York (1977)

    MATH  Google Scholar 

  9. Maillert, L., Bernard, O., Steyer, J.-P.: Robust regulation of anaerobic digestion processes. Water Sci. Technol. 48(6), 87–94 (2003)

    Google Scholar 

  10. Ruan, S.: On nonlinear dynamics of predator-prey models with discrete delay. Math. Model. Nat. Phenom. 4(2), 140–188 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. Ruan, S., Wei, J.: On the zeroes of transcendental functions with applications to stability of delay differential equations. Dynam. Contin. Impuls. Syst. 10, 863–874 (2003)

    MathSciNet  MATH  Google Scholar 

  12. Smith, H.: An Introduction to Delay Differential Equations with Applications to the Life Sciences. exts in Applied Mathematics, vol. 57. Springer, New York (2011)

    MATH  Google Scholar 

  13. Wang, L., Wolkowicz, G.: A delayed chemostat model with general nonmonotone response functions and differential removal rates. J. Math. Anal. Appl. 321, 452–468 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  14. Wolkowicz, G., Xia, H.: Global asymptotic behavior of a chemostat model with discrete delays. SIAM J. Appl. Math. 57(4), 1019–1043 (1997)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Neli S. Dimitrova .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Borisov, M.K., Dimitrova, N.S., Krastanov, M.I. (2015). Functional Differential Model of an Anaerobic Biodegradation Process. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2015. Lecture Notes in Computer Science(), vol 9374. Springer, Cham. https://doi.org/10.1007/978-3-319-26520-9_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-26520-9_10

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-26519-3

  • Online ISBN: 978-3-319-26520-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics