Chaos in a periodically forced chemostat with algal mortality

Proceedings of the Royal Society B: Biological Sciences

Volumn 271, Issue 1548, 2004, Pages 1617-1624

  Clodong, Sébastien ^a   Blasius, Bernd ^a  

^a UNIVERSITY OF POTSDAM   (Germany)

Author keywords

Algal mortality; Chaos; Chemostats; Droop model; Nutrient limited algal growth; Periodically forced system

Indexed keywords

CHAOS THEORY; CHEMOSTAT; MORTALITY; NUTRIENT AVAILABILITY; PHYTOPLANKTON;

ARTICLE; CHAOTIC DYNAMICS; CHEMOSTAT; MORTALITY; NUTRIENT SUPPLY; OSCILLATION; PHYTOPLANKTON; POPULATION MODEL; PRIORITY JOURNAL;

ALGAE;

EID: 3242884781     PISSN: 09628452     EISSN: 14712970     Source Type: Journal    
DOI: 10.1098/rspb.2004.2767     Document Type: Article

References (33)

1. Blasius, B. & Stone, L. 2000 Chaos and phase synchronization in ecological systems. Int. J. Bifurc. Chaos 10, 2361-2380.
2. Blasius, B., Huppert, A. & Stone, L. 1999 Complex dynamics and phase synchronization in spatially extended ecological systems. Nature 399, 354-359.
3. Costantino, R. F., Desharnais, R. A., Cushing, J. M. & Dennis, B. 1997 Chaotic dynamics in an insect population. Science 275, 389-391.
4. Cushing, J. M., Costantino, R. F., Dennis, B., Desharnais, R. A. & Henson, S. M. 2003 Chaos in ecology: experimental nonlinear dynamics. Amsterdam: Academic.
5. DeAngelis, D. L. 1992 Dynamics of nutrient cycling and food webs. London: Chapman & Hall.
6. Dennis, B., Desharnais, R. A., Cushing, J. M., Henson, S. M. & Costantino, R. F. 2003 Can noise induce chaos? Oikos 102, 329-339.
7. 12 and marine ecology. IV. The kinetics of uptake, growth and inhibition in Monochrysis lutheri. J. Mar. Biol. Assoc. UK 48, 689-733.
8. Droop, M. R. 1973 Some thoughts on nutrient limitation in algae. J. Phycol. 9, 264-272.
9. Earn, D. J. D., Rohani, P., Bolker, B. M. & Grenfell, B. T. 2000 A simple model for complex dynamical transitions in epidemics. Science 287, 667-670.
10. Ebenhöh, W. 1988 Coexistence of an unlimited number of algal species in a model system. Theor. Popul. Biol. 34, 130-144.
11. Ebenhoh, W. 1993 Coexistence of similar species in models with periodic environments. Ecol. Model. 68, 227-247.
12. Fussmann, G. F., Ellner, S. P., Shertzer, K. W. & Hairston Jr, N. G. 2000 Crossing the Hopf bifurcation in a live predator-prey system. Science 290, 1358-1360.
13. Grover, J. P. 1991a Non-steady state dynamics of algal population growth: experiments with two chlorophytes. J. Phycol. 27, 70-79.
14. Grover, J. P. 1991b Dynamics of competition among microalgae in variable environments: experimental tests of alternative models. Oikos 62, 231-243.
15. Hastings, A. & Powell, T. 1991 Chaos in a three-species food chain. Ecology 72, 896-903.
16. Hastings, A., Hom, C. L., Ellner, S., Turchin, P. & Godfray, H. C. J. 1993 Chaos in ecology: is Mother Nature a strange attractor? A. Rev. Ecol. Syst. 24, 1-33.
17. Huisman, J. & Weissing, F. J. 1999 Biodiversity of plankton by species oscillations and chaos. Nature 402, 407-410.
18. Huppert, A., Blasius, B. & Stone, L. 2002 A model of phytoplankton blooms. Am. Nat. 159, 156-171.
19. Hutchinson, G. E. 1961 The paradox of the plankton. Am. Nat. 95, 137-145.
20. Kot, M., Sayler, G. S. & Schultz, T. W. 1992 Complex dynamics in a model microbial system. Bull. Math. Biol. 54, 619-648.
21. Lange, K. & Oyarzun, F. J. 1992 The attractiveness of the Droop equations. Math. Biosci. 111, 261-278.
22. May, R. M. 1974 Biological populations with non-overlapping generations: stable points, stable cycles, and chaos. Science 186, 645-647.
23. Monod, J. 1942 Recherches sur la croissance des cultures bactériennes. Paris: Hermann.
24. O'Brien, W. J. 1974 The dynamics of nutrient limitation of phytoplankton algae: a model reconsidered. Ecology 55, 135-141.
25. Pascual, M. 1994 Periodic response to periodic forcing of the Droop equations for phytoplankton growth. J. Math. Biol. 32, 743-759.
26. Rinaldi, S. & Muratori, S. 1993 Conditioned chaos in seasonally perturbed predator-prey models. Ecol. Model. 69, 79-97.
27. Smith, H. L. 1997 The periodically forced Droop model for phytoplankton growth in a chemostat. J. Math. Biol. 35, 545-556.
28. Smith, H. L. & Waltman, P. 1995 The theory of the chemostat: dynamics of microbial competition. New York: Cambridge University Press.
29. Sommer, U. 1985 Comparison between steady state and non-steady state competition: experiments with natural populations. Limnol. Oceanogr. 30, 335-346.
30. Truscott, J. E. 1995 Environmental forcing of simple plankton models. J. Plankt. Res. 17, 2207-2232.
31. Vandermeer, J., Stone, L. & Blasius, B. 2001 Categories of chaos and fractal basin boundaries in forced predator-prey models. Chaos, Solitons Fractals 12, 265-276.
32. Wolf, A., Swift, J. B., Swinney, H. L. & Vastano, J. A. 1985 Determining Lyapunov exponents from a time series. Physica D 16, 285-317.
33. Yoshida, T., Jones, L. E., Ellner, S. P., Fussmann, G. F. & Hairston, N. G. 2003 Rapid evolution drives ecological dynamics in a predator-prey system. Nature 424, 303-306.