Comparisons, by models, of some basic mechanisms acting on the dynamics of the zooplankton-toxic phytoplankton system

Mathematical Models and Methods in Applied Sciences

Volumn 12, Issue 10, 2002, Pages 1421-1451

  El Abdllaoui, A ^a   Chattopadhyay, J ^b   Arino, Ovide ^c  

^a FACULTÉ DES SCIENCES   (Morocco)

^b INDIAN STATISTICAL INSTITUTE   (India)

^c Centre de Recherche d'Ile de France   (France)

Author keywords

Bloom; Chain trick; Hopf Bifurcation; Infinite delay; Poincar map; Routh Hurwitz; Toxic phytoplankton; Zooplankton

Indexed keywords

EID: 0036812105     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202502002185     Document Type: Article

References (31)

1. J. Aure and F. Rey, Oceanographic conditions in the Sandsfjord system, western Norway, after a bloom of the prymnesiophyte Prymnesium parvum, Sarsia 76 (1992) 247-254.
2. D.G. Baden et al., Brevetoxin analysis. Toxic dinoflagllates and marine mammal mortalities, Technical Reports Woods Hole Oceanographic Institution (1989) 47-52.
3. E. Beretta, G.I. Bischi and F. Solimano, Stability in chemostat equations with delayed nutrient recycling, J. Math. Biol. 28 (1990) 99-111.
4. T.A. Burton, Volterra Integral and Differential Equations (Academic Press, 1983).
5. B.D. Coleman and V.J. Mizel, Norms and semigraups in the theory of fading memory, Arch. Rational. Mech. Anal. 2 (1966) 87-123.
6. J.M. Cushing, Integrodifferential Equations and Delay Models in Population Dynamics (Springer-Verlag, 1977).
7. F. Doveri, M. Scheffer, S. Rinaldi, S. Muratori and Y.A. Kutzenov, Seasonality and chaos in a plankton-fish model, Theor. Pop. Biol. 43 (1993) 159-183.
8. A.M. Edward and J. Brindley, Oscillatory behaviour in a three-component plankton population model, Dynamic Stability Systems 11 (1996) 347-370.
9. A.M. Edward and J. Brindley, Zooplankton mortality and the dynamical behaviour of plankton population models, Bull. Math. Biol. 61 (1999) 303-339.
10. P. Fay, in The Blue-Greens (Edward Arnold Ltd., 1983).
11. J. Haddock and T. Kristzin, Rate of decay of solutions of functional differential equations with infinite delay, Nonlinear Anal. 10 (1986) 727-742.
12. J. Hale and J. Kato, Phase space for retarded equations with infinite delay, Funk. Ekvac. 21 (1978) 11-41.
13. J. Hale and Verduyn Lunel, Introduction to Functional Differential Equations, Appl. Math. Sci., Vol. 99 (Springer-Verlag, 1993).
14. G.M. Hallegraeff, A review of harmful algae blooms and the apparent global increase, Phycologia 32 (1993) 79-99.
15. B.D. Hassard, N.D. Kazarinoff and Y.H. Wan, Theory and Applications of Hopf Bifurcation (1981).
16. Y. Hino, S. Murakamai and T. Naito, Functional Differential Equations with Infinite Delay, Lecture Notes in Math., Vol. 1473 (Springer-Verlag, 1991).
17. S.A. Levin and L. Segel, Hypothesis for the origin of plankton patchiness, Nature 259 (1976) 659.5.
18. N. MacDonald, Time Lags in Biological Models, Lecture Notes in Biomathematics, Vol. 27 (Springer-Verlag, 1978).
19. L. Mathews and J. Brindley, Patchiness in plankton populations, Dynamics and Stability Systems 12 (1996) 39-59.
20. J.D. Murray, Mathematical Biology (Springer-Verlag, 1990).
21. T.G. Nielsen et al., Effects of Chrysochromulina polylepis subsurface bloom on the plankton community, Marine Ecol. Prog. Series 62 (1990) 21-35.
22. J.H. Pitchford and E.W. Henderson, Intratrophic predation in simple predator-prey models, Bull. Math. Biol. 60 (1998) 937-953.
23. S. Ruan, Turing instability and travelling waves in diffusive plankton models with delayed nutrient recycling, IMA J. Appl. Math. 61 (1998) 15-32.
24. M. Scheffer, Should we expect strange attractors behind plankton dynamics, and if so, should we bother? J. Plankton Res. 13 (1991) 1291-1305.
25. J.H. Steele and E.W. Henderson, The significance of interannual variability, in Towards a Model of Ocean Biogeochemical Processes, eds. G.T. Evans and M.J.R. Fasham (Springer-Verlag, 1993), pp. 237-260.
26. K.A. Steidinger et al., P.fisteria Piscicida, a new toxic dinoflagllate genus and species of the order Dinamoebales, J. Phycology 32 (1996) 157-164.
27. J.E. Truscott and J. Brindley, Ocean plankton populations excitable media, Bull. Math. Biol. 56 (1994) 981-998.
28. S. Uye, Impact of copepod grazing on the red tide flagellate Chattonella antiqua, Mar. Biol. 92 (1986) 35.
29. G. Wake et al., Picoplankton and marine food chain dynamics in a variable mixed layer reaction-diffusion model, Ecol. Modelling 57 (1991) 193.
30. G. Wolkowicz et al., Global dynamics of a chemostat competition model with distributed delay, J. Math. Biol. 38 (1999) 285-316.
31. T. Wyatt and J. Horwood, Model which generates red tides, Nature 244 (1973) 238-240.