Modeling migratory grazing of zooplankton on toxic and non-toxic phytoplankton

Applied Mathematics and Computation

Volumn 197, Issue 2, 2008, Pages 659-671

  Chowdhury, Tanmay ^a   Roy, Shovonlal ^a   Chattopadhyay, J ^a  

^a INDIAN STATISTICAL INSTITUTE   (India)

Author keywords

Aggregation method; Density dependent migrations; Equilibria; Limit cycle; Non equilibria; Stability; Toxin producing phytoplankton

Indexed keywords

AGGLOMERATION; ENZYME INHIBITION; MATHEMATICAL MODELS; TOXIC MATERIALS;

DENSITY DEPENDENT MIGRATIONS; LIMIT CYCLE; MIGRATORY GRAZING; TOXIN PRODUCING PHYTOPLANKTONS; ZOOPLANKTON;

PHYTOPLANKTON;

EID: 39449108384     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2007.08.004     Document Type: Article

References (15)

1. Chattopadhyay J., Sarkar R.R., and Mandal S. Toxin-producing plankton may act as a biological control for planktonic blooms - field study and mathematical modelling. J. Theor. Biol. 215 (2002) 333
2. Kirk K., and Gilbert J. Variation in herbivore response to chemical defence: zooplankton foraging on toxic cynobacteria. Ecology 73 (1992) 2208
3. Kozlowsky-Suzuki B., et al. Feeding, reproduction and toxin accumulation by the copepods Acartia bifilosa and Eurytenora affinis in the presence of the toxic cynobacterium Nodularia Spumigena. Mar. Ecol. Prog. 249 (2003) 237
4. Sarkar R.R., and Chattopadhayay J. The role of environmental stochasticity in a toxic phytoplankton-non-toxic phytoplankton-zooplankton system. Environmetrics 14 (2003) 775 10.1002/env.621
5. Roy S., Alam S., and Chattopadhyay J. Competitive effects of toxin-producing phytoplankton on the overall plankton populations in the Bay of Bengal. Bull. Math. Biol. 68 8 (2006) 2303
6. Roy S., and Chattopadhyay J. Toxin-allelopathy among phytoplankton species prevents competitive exclusion. J. Biol. Syst. 15 1 (2007) 73
7. Chiorino G., Auger P., Chasse J.-L., and Charles S. Behavioral choices based on patch selection: a model using aggregation methods. Math. Biosci. 157 (1999) 189
8. Mchich R., Auger P.M., and Poggiale J.-C. Effect of predator density dependent dispersal of prey on stability of a predator-prey system. Math. Biosci. 206 2 (2007) 343
9. Andersen V., Gubanova A., Nival P., and Ruellet T. Zooplankton community during the transition from spring bloom to oligotrophy in the open NW Mediterranean and effects of wind events. 2. Vertical distributions and migrations. J. Plankton Res. 23 3 (2001) 243
10. Slusarczyck M., Dawidowicz P., and Rygielska E. Hide, rest or die: a light-mediated diapause response in Daphnia magma to the threat of fish predation. Freshwater Biol. 50 1 (2005) 141
11. Auger P.M., and Roussarie R. Complex ecological models with simple dynamics: from individuals to populations. Acta Biotheor. 42 (1994) 111
12. Auger P.M., and Poggiale J.-C. Aggregation and emergence in systems of ordinary differential equation. Math. Comput. Modell. 27 4 (1998) 1
13. Michalski J., Poggiale J.-C., Arditi R., and Auger P.M. Macroscopic dynamic effects of migration in patchy predator-prey systems. J. Theor. Biol. 185 (1997) 459
14. Ludwig D., et al. Qualitative analysis of an insect outbreak system: the sruce budworm and forest. J. Animal. Ecol. 47 (1978) 315
15. Birkhoff G., and Rota G.C. Ordinary Differential Equation (1982), Ginn, Boston