The dynamic of plankton-nutrient interaction with delay

In this paper we consider the plankton-nutrient interaction model with the help of delay differential equations. Firstly the elementary dynamical properties of the plankton-nutrient system in the absence of time delay is discussed. Then we establish the existence of local Hopf-bifurcation as the time delay crosses a 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 and complex dynamic of the system is explored with the existence of chaotic attractors.