Dynamics of a marine plankton system: Diffusive instability and pattern formation

Applied Mathematics and Computation

Volumn 218, Issue 17, 2012, Pages 8895-8905

  Gazi, Nurul Huda ^a  

^a Aliah University   (India)

Author keywords

Constant and periodic diffusions; Hill's equation; Reaction diffusion system; Stability; Turing space

Indexed keywords

ANALYTICAL RESULTS; FUNCTIONAL RESPONSE; HILL'S EQUATION; MARINE PLANKTONS; PATTERN FORMATION; PREY-PREDATOR; REACTION DIFFUSION EQUATIONS; REACTION DIFFUSION SYSTEMS; REACTION-DIFFUSION SYSTEM; STABILITY BEHAVIOR; TEMPORAL VARIATION; TURING SPACE;

CONVERGENCE OF NUMERICAL METHODS; DIFFUSION; DYNAMIC MODELS; LINEAR EQUATIONS; MARINE BIOLOGY; PHYTOPLANKTON;

STABILITY;

EID: 84859432037     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2012.02.048     Document Type: Article

References (33)

1. M. Bandyopadhyay, and R. Bhattacharya A Nonlinear two-species oscillatory system: bifurcation and stability analysis Int. J. Math. Math. Sci. 31 2003 1981 1991
2. R. Bhattacharya, B. Mukhopadhyay, and M. Bandyopadhyay Deffisive instability in a prey-predator system with time dependent diffusivity Int. J. Math. Math. Sci. 66 2003 4195 4203
3. E.J. Buskey, and D.A. Stockwell Effects of a persistent 'brown tide' on zooplankton population in the Laguna Madre of Southern Texas T.J. Smayda, Y. Shimuzu, Toxic Phytoplankton Blooms in the Sea 1993 Elsevier Amsterdam 659 666
4. J. Chattopadhyay, R.R. Sarkar, and A.El. Abdllaoui A delay differential equation model on harmful algal blooms in the presence of toxic substances IMA J. Math. Appl. Med. Biol. 19 2002 137 161
5. D.H. Cushing The vertical migration of planktonic crustacea Biol. Rev. 26 1951 158 192
6. CO 2-problem und die Rolle des Ozeans. Naturwissenschahten 81 1993 237 242
7. L. Edelstein-Keshet Mathematical Models in Biology The Random House/Birkhäuser Mathematics Series 1988 Random House New York
8. K.W. Estep, J.C. Nejstgaard, H.R. Skjoldal, and F. Rey Predation by copepods upon natural populations of Phaeocystis pouchetti as a function of physiological state of the prey Mar. Ecol. Prog. Ser. 67 1990 235 249
9. P. Fay The Blue-Greens 1983 Arnold London
10. N.H. Gazi, and M. Bandyopadyay Effect of time delay on a detritus-based ecosystem Int. J. Math. Math. Sci. 2006 2006 1 28
11. P. Grinrod The Theory and Applications of Reaction-Diffusion Equations, Patterns and Waves Oxford Applied Mathematics and Computing Science Series 1996 The Clarendon Press, Oxford University Press New York
12. T.G. Hallam Mathematical Ecology T.G. Hallam, S.A. Levin, 1983 Springer Verlag Berlin
13. F.C. Hansen Trophic interaction between zooplankton and Phaeocystis cf. Globosa Helgol Meeresunters 49 1990 283 293
14. V.S. Ivlev Experimental Ecology of the Feeding of Fishes 1961 Yale University Press New Hacen
15. K.I. Keating, 1976, Algal metabolite influence on bloom sequence in eutrophic freshwater ponds, E.P.A., Ecological Monograph Series (EPA. 600/3-76-081. Washington, DC), 1976, p. 148.
16. K. Kirk, and J. Gilbert Variation in herbivore response to chemical defences: zooplankton foraging on toxic cynobacteria Ecology 73 1992 2208
17. W. Lampert Zooplankton vertical migration: implications for phytoplankton-zooplankton interactions Arch. Hydrobiol. Beih. Ergebn. Limnol. 35 1992 69 78
18. W. Magnus, and S. Winkler Hill's Equation 1979 Dover New York
19. A. Maiti, M.M. Jana, and G.P. Samanta Deterministic and stochastic analysis of a ratio-dependent of a prey-predator system with delay Nonlinear Anal.: Model. Control 12 3 2007 383 398
20. A.Yu. Morozov, S.V. Petrovskii, and N.P. Nezlin Towards resolving the paradox of enrichment: the impact of zooplankton vertical migrations on plankton system stability J. Theo. Biol. 248 2007 501 511
21. B. Mukhopadhyay, and R. Bhattacharya A delay-diffusion model of marine plankton ecosystem exhibiting cyclic nature of blooms J. Biol. Phys. 31 2005 3 22
22. J.D. Murray Mathematical Biology 2002 Springer-Verlag Berlin
23. M. Ohman The demographic benefits of diel vertical migration by zooplankton Am. Nat. 60 1990 257 281
24. A. Okubo Diffusion and Ecological Problems: Modern Perspective Interdisciplinary Applied Mathematics 14 2001 Springer Berlin
25. M.L. Rosenzweig, and R.H. MacArthur Graphical representation and stability conditions of predator-prey interactions Am. Nat. 97 1963 209 223
26. G.P. Samanta Stochastic analysis of a prey-predator system I.J. Math. Edu. Sc. Tech. 25 6 1994 797 803
27. L.A. Segal, and J.L. Jackson Dissipative structure: an explanation and ecological example J. Theor. Biol. 37 1972 545 559
28. S. Sjoberge Are pelagic systems inherently unstable? A model study Ecol. Model. 3 1977 17 37
29. J.H. Steele Structure of Marine Ecosystems 1974 Blackwell Scientific Oxford
30. A.J. Taylor Characteristic properties of model for the vertical distributions of phytoplankton under stratification Ecological modelling 40 1988 175 199
31. A.M. Turing The chemical basis of morphogenesis Phil. Trans. R. Soc. Lond. B 237 1952 37 72
32. M.E. Vinogradov, Vertical distribution of the oceanic zooplankton, Israeli Program for Scientific Translations, Jerusalem, 1970.
33. J.S. Wroblewski, J.L. Sarmiento, and G.R. Flierl An ocean basin scale model of plankton dynamics in the North Atlantic, 1. Solutions for the climatological oceanographic condition in May, Global Biogeochem Cycles 2 1988 199 218