Role of dissolved oxygen on the plankton dynamics in spatio-temporal domain

Abstract

A mathematical model is proposed to study the role of dissolved oxygen in the plankton ecosystem in spatiotemporal domain, considering one nonliving compartment, i.e., dissolved oxygen and two living compartments, i.e., phytoplankton and zooplankton populations with Holling type II response function for the harvesting rate of phytoplankton by zooplankton population. In temporal system, the local stability analysis of all the feasible equilibria is studied and also explored the existence of Hopf-bifurcation for the interior equilibrium, taking the growth rate of phytoplankton as bifurcation parameter. Further, the direction of Hopf-bifurcation and stability of the bifurcating periodic solutions are presented using normal form theory. In spatial system, we have obtained the condition for diffusion driven instability and obtained different types of spatial patterns with different step size in time. Furthermore, conducted the higher-order stability analysis of the spatiotemporal dynamics. Finally, numerical simulation is given in support of the analytic results for both temporal and spatiotemporal domain.