Rich dynamics of non-toxic phytoplankton, toxic phytoplankton and zooplankton system with multiple gestation delays
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The plankton community is classified into three category of species, namely, non-toxic phytoplankton (NTP), toxic phytoplankton (TPP) and zooplankton. In this work we have introduced a mathematical model for the interaction of NTP, TPP and zooplankton population in an open marine system. We have incorporated two time delays and observed important mathematical characteristics of the proposed model such as positivity, boundedness, stability and Hopf-bifurcation for all possible combinations of both the delays at the interior equilibrium point of the model system. It is noted that increase in gestation delay may lead to the destabilization of stationary points through the creation of limit cycles. Various numerical simulations are performed to validate the analytical findings obtained here.
KeywordsPhytoplankton Zooplankton Stability Permanence Hopf-bifurcation
The authors are grateful to the anonymous referees and Editor in Chief Prof. Jian-Qiao Sun for their careful reading, valuable comments and helpful suggestions, which have helped them to improve the presentation of this work significantly. The first author (Ashok Mondal) is thankful to the University Grants Commission, India for providing SRF (RGNF). The second author (A. K. Pal) acknowledges financial support from UGC, India (MRP No.-PSW-128/15-16 (ERO)).
- 3.Anderson DM (1989) Toxic algae blooms and red tides: a global perspective. In: Okaichi T, Anderson DM, Nemoto T (eds) Red tides biology, environmental science and toxicology. Elsevier, New York, pp 11–16Google Scholar
- 5.Smayda T (1990) Novel and nuisance phytoplankton blooms in the sea: evidence for a global epidemic. In: Graneli E, Sundstrom B, Edler L, Anderson DM (eds) Toxin marine phytoplankton. Elsevier, New York, pp 29–40Google Scholar
- 6.Blaxter JHS, Southward AJ (1997) Advance in marine biology. Academic Press, LondonGoogle Scholar
- 17.Mondal S, Maiti A, Samanta GP (2018) Effects of fear and additional food in a delayed predator–prey model. Biophys Rev Lett. https://doi.org/10.1142/S1793048018500091
- 24.Mondal A, Pal AK, Samanta GP (2018) On the dynamics of evolutionary Leslie–Gower predator–prey eco-epidemiological model with disease in predator. Ecol Genet Genom. https://doi.org/10.1016/j.egg.2018.11.002
- 26.Sangeeta S, Samanta GP (2018) Influence of dispersal and strong Allee effect on a two-patch predator–prey model. Int J Dyn Control. https://doi.org/10.1007/s40435-018-0490-3
- 31.Gard TC, Hallam TG (1979) Persistence in food web-1, Lotka–Voltterra food chains. Bull Math Biol 41:302–315Google Scholar