Abstract: In this paper, for the understanding of the phytoplankton dynamics in marine ecosystem, a susceptible and an infected class of phytoplankton population is considered in spatiotemporal domain.
Here, the susceptible phytoplankton is growing logistically and the
growth of infected phytoplankton is due to the instantaneous Holling
type-II infection response function. The dynamics are studied in terms of the local and global stabilities for the system and further
explore the possibility of Hopf -bifurcation, taking the half saturation period as (i.e., ) the bifurcation parameter in temporal domain.
It is also observe that the reaction diffusion system exhibits spatiotemporal
chaos and pattern formation in phytoplankton dynamics,
which is particularly important role play for the spatially extended phytoplankton system. Also the effect of the diffusion coefficient
on the spatial system for both one and two dimensional case is obtained. Furthermore, we explore the higher-order stability analysis
of the spatial phytoplankton system for both linear and no-linear system. Finally, few numerical simulations are carried out for pattern
formation.