Non-linear qualitative signal processing for biological systems: Application to the algal growth in bioreactors

Mathematical Biosciences

Volumn 157, Issue 1-2, 1999, Pages 357-372

  Bernard, Olivier ^a   Gouzé, Jean Luc ^b  

^a UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

^b INRIA   (France)

Author keywords

Algal growth; Bioreactor; Moving average; Non linear systems; Qualitative behavior; Validation

Indexed keywords

ALGA; BIOLOGICAL MODEL; BIOREACTOR; CONFERENCE PAPER; ECOSYSTEM; MATHEMATICAL ANALYSIS; NONHUMAN; NONLINEAR SYSTEM; PLANT GROWTH;

ALGAE; BIOREACTORS; COMPUTER SIMULATION; LINEAR MODELS; MODELS, BIOLOGICAL; PHYTOPLANKTON; SIGNAL PROCESSING, COMPUTER-ASSISTED;

EID: 0032936159     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0025-5564(98)10091-3     Document Type: Conference Paper

References (21)

1. Banks H., Mahaffy J. Stability of cyclic gene models in systems involving repression. J. Theoretical Biol. 74:1978;323.
2. G. Bastin, D. Dochain, On-line Estimation and Adaptative Control of Bioreactors, Elsevier, Amsterdam, 1990.
3. O. Bernard, Etude expérimentale et théorique de la croissance de Dunaliella tertiolecta (chlorophyceae) soumise à une limitation variable de nitrate: utilisation de la dynamique transitoire pour la conception et la validation des modèles, PhD thesis, University Pierre et Marie Curie, Paris VI, 1995.
4. Bernard O., Gouzé J.-L. Transient behavior of biological loop models, with application to the Droop model. Math. Biosci. 127:1995;19.
5. Bernard O., Malara G., Sciandra A. The effects of a controlled fluctuating nutrient environment on continuous cultures of phytoplankton monitored by a computer. J. Exp. Mar. Biol. Ecol. 197:1996;263.
6. Burmaster D.E. The unsteady continuous culture of phosphate-limited Monochrysis lutheri Droop: experimental and theoretical analysis. J. Exp. Mar. Biol. Ecol. 39(2):1979;167.
7. Cohen M.A., Levine D.S. Unbounded oscillations solutions for a system of interacting populations. SIAM J. Appl. Math. 45:1985;268.
8. Droop M.R. Vitamin B12 and marine ecology. IV. The kinetics of uptake growth and inhibition in Monochrysis lutheri. J. Mar. Biol. Assoc. 48(3):1968;689.
9. B.C. Goodwin. Oscillatory behavior in enzymatic control processes, in: G. Weber (Ed.), Advances in Enzyme Regulation, vol. 3, Pergamon, Oxford, 1965, p. 425.
10. Hastings S., Tyson J., Webster D. Existence of periodic solutions for negative feedback control systems. J. Differential Equations. 25:1977;39.
11. J. Hofbauer, K. Sigmund, The theory of evolution and dynamical systems, Cambridge University, Cambridge, 1988.
12. Klein P., Coste B. Effects of wind-stress variability on a nutrient transport into the mixed layer. Deep Sea Res. 31:1984;21.
13. L. Ljung. System Identification: Theory for the User, Prentice-Hall, Englewood Cliffs, NJ, 1987.
14. Mallet-Paret J., Smith H. The Poincaré-Bendixson theorem for monotone cyclic feedback systems. J. Dyn. Different. Eq. 2(4):1990;367.
15. J. Murray, Mathematical Biology, Springer, Berlin, 1990.
16. Oyarzun F.J., Lange K. The attractiveness of the Droop equations II: generic uptake and growth functions. Math. Biosci. 121:1994;127.
17. Pascual M. Periodic response to periodic forcing of the Droop equations for phytoplankton growth. J. Math. Biol. 32:1994;743.
18. Smith H. The periodically forced Droop model for phytoplankton growth in the chemostat. J. Math. Biol. 35:1997;545.
19. R. Thomas (Ed.), Kinetic Logic, Lecture Notes in Biomathematics, vol. 29, Springer, Berlin, 1979.
20. E. Walter, L. Pronzato, Identification of parametric models from experimental data, Springer, Berlin, 1997.
21. Wroblewski J.S. Interaction of currents and vertical migration in maintaining Calanus marshallae in the Oregon upwelling zone - a simulation. Deep Sea Res. 29:1982;665.