Role of Delay on Planktonic Ecosystem in the Presence of a Toxic Producing Phytoplankton
A mathematical model is proposed to study the role of distributed delay on plankton ecosystem in the presence of a toxic producing phytoplankton. The model includes three state variables, namely, nutrient concentration, phytoplankton biomass, and zooplankton biomass. The release of toxic substance b...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
|
| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2011/603183 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832567097449775104 |
|---|---|
| author | Swati Khare O. P. Misra Chhatrapal Singh Joydip Dhar |
| author_facet | Swati Khare O. P. Misra Chhatrapal Singh Joydip Dhar |
| author_sort | Swati Khare |
| collection | DOAJ |
| description | A mathematical model is proposed to study the role of distributed delay on plankton ecosystem in the presence of a toxic producing phytoplankton. The model includes three state variables, namely, nutrient concentration, phytoplankton biomass, and zooplankton biomass. The release of toxic substance by phytoplankton species reduces the growth of zooplankton and this plays an important role in plankton dynamics. In this paper, we introduce a delay (time-lag) in the digestion of nutrient by phytoplankton. The stability analysis of all the feasible equilibria are studied and the existence of Hopf-bifurcation for the interior equilibrium of the system is explored. From the above analysis, we observe that the supply rate of nutrient and delay parameter play important role in changing the dynamical behaviour of the underlying system. Further, we have derived the explicit algorithm which determines the direction and the stability of Hopf-bifurcation solution. Finally, numerical simulation is carried out to support the theoretical result. |
| format | Article |
| id | doaj-art-545903954df34a9692cac8ba83c9a1e7 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-545903954df34a9692cac8ba83c9a1e72025-02-03T01:02:18ZengWileyInternational Journal of Differential Equations1687-96431687-96512011-01-01201110.1155/2011/603183603183Role of Delay on Planktonic Ecosystem in the Presence of a Toxic Producing PhytoplanktonSwati Khare0O. P. Misra1Chhatrapal Singh2Joydip Dhar3School of Mathematics and Allied Sciences, Jiwaji University, MP Gwalior 474011, IndiaSchool of Mathematics and Allied Sciences, Jiwaji University, MP Gwalior 474011, IndiaSchool of Mathematics and Allied Sciences, Jiwaji University, MP Gwalior 474011, IndiaDepartment of Applied Sciences, ABV-Indian Institute of Information Technology and Management, MP Gwalior 474010, IndiaA mathematical model is proposed to study the role of distributed delay on plankton ecosystem in the presence of a toxic producing phytoplankton. The model includes three state variables, namely, nutrient concentration, phytoplankton biomass, and zooplankton biomass. The release of toxic substance by phytoplankton species reduces the growth of zooplankton and this plays an important role in plankton dynamics. In this paper, we introduce a delay (time-lag) in the digestion of nutrient by phytoplankton. The stability analysis of all the feasible equilibria are studied and the existence of Hopf-bifurcation for the interior equilibrium of the system is explored. From the above analysis, we observe that the supply rate of nutrient and delay parameter play important role in changing the dynamical behaviour of the underlying system. Further, we have derived the explicit algorithm which determines the direction and the stability of Hopf-bifurcation solution. Finally, numerical simulation is carried out to support the theoretical result.http://dx.doi.org/10.1155/2011/603183 |
| spellingShingle | Swati Khare O. P. Misra Chhatrapal Singh Joydip Dhar Role of Delay on Planktonic Ecosystem in the Presence of a Toxic Producing Phytoplankton International Journal of Differential Equations |
| title | Role of Delay on Planktonic Ecosystem in the Presence of a Toxic Producing Phytoplankton |
| title_full | Role of Delay on Planktonic Ecosystem in the Presence of a Toxic Producing Phytoplankton |
| title_fullStr | Role of Delay on Planktonic Ecosystem in the Presence of a Toxic Producing Phytoplankton |
| title_full_unstemmed | Role of Delay on Planktonic Ecosystem in the Presence of a Toxic Producing Phytoplankton |
| title_short | Role of Delay on Planktonic Ecosystem in the Presence of a Toxic Producing Phytoplankton |
| title_sort | role of delay on planktonic ecosystem in the presence of a toxic producing phytoplankton |
| url | http://dx.doi.org/10.1155/2011/603183 |
| work_keys_str_mv | AT swatikhare roleofdelayonplanktonicecosysteminthepresenceofatoxicproducingphytoplankton AT opmisra roleofdelayonplanktonicecosysteminthepresenceofatoxicproducingphytoplankton AT chhatrapalsingh roleofdelayonplanktonicecosysteminthepresenceofatoxicproducingphytoplankton AT joydipdhar roleofdelayonplanktonicecosysteminthepresenceofatoxicproducingphytoplankton |