Bifurcation analysis of a plankton model with Discrete Delay(#Third Revision, paper code JRNL6919)
| Main Authors: | Anuj K. Sharma, Amit Sharma, Kulbhushan Agnihotri |
|---|---|
| Format: | Article Journal |
| Bahasa: | eng |
| Terbitan: |
, 2013
|
| Online Access: |
https://zenodo.org/record/2659923 |
Daftar Isi:
- In this paper, a delayed plankton-nutrient interac- tion model consisting of phytoplankton, zooplankton and dis- solved nutrient is considered. It is assumed that some species of phytoplankton releases toxin (known as toxin producing phyto- plankton(TPP)) which is harmful for zooplankton growth and this toxin releasing process follows a discrete time variation. Using delay as bifurcation parameter, the stability of interior equilibrium point is investigated and it is shown that time delay can destabilise the otherwise stable non-zero equilibrium state by inducing Hopf-bifurcation when it crosses a certain threshold value. Explicit results are derived for stability and direction of the bifurcating periodic solution by using normal form theory and center manifold arguments. Finally, outcomes of the system are validated through numerical simulations.