Chaos Control in a Time Delayed Phytoplankton-Zooplankton System with Harvesting of Zooplankton

In this paper, a mathematical model with two classes of population namely phytoplankton-zooplankton system is proposed. It has been assumed that predator thrives completely on predation of prey, viz., phytoplankton population. The rate of predation is addressed by Holling type II function response. Remarkably, growth rate, predation rate, handling time, conversion rate, death rate, and Holling parameter are considered to be realistic, which makes the model different from those in the existing related literature. The model possesses three ecologically feasible steady states (i) both the species going to extinction, (ii) predator population going to extinction and survival of the prey population, and (iii) both the species are coexisting. To explore the system dynamics in absence of time delay, the stability analysis is done for all the steady states. The local stability conditions are investigated for the coexisting equilibrium point of a time delayed system. By examining the characteristic equation, the existence of Hopf bifurcation has been observed with respect to critical parameter τ. The system dynamics is sensitive to time delay parameter and is highly responsible in bringing about chaotic situations. Further, the harvesting rate of zooplanktons is helpful in chaos control in the system. At last, the numerical simulations have been done to justify the analytical findings.