Complex Dynamics of Phytoplankton-Zooplankton Interaction System with Predation and Toxication Delay

Abstract

In this manuscript, we propose a two-dimensional complex plankton dynamics of phytoplankton and zooplankton interacting species to investigate the impact of multiple delays, viz., predation and toxin liberation delay. We consider predation delay (PD) in the zooplankton population and toxin liberation delay (TLD) in both populations namely, the phytoplankton and zooplankton species. It is observed that the given system is bounded and positive with and without delay under certain conditions. The conditional local and global stabilities of different equilibrium points are obtained. The stability and instability of the delayed system have been discussed analytically and numerically to show the existence of Hopf-bifurcation and its properties for all possible combinations of both delays about the positive equilibrium of the plankton system. The study of different parameters has been carried out to discuss the occurrence and non-occurrence of planktonic blooms. It is concluded that variation in zooplankton predation delay and toxin liberation delay may lead to unstable the plankton system through the existence of periodic oscillations with the occurrence of planktonic blooms.