Delay-induced nutrient recycling in plankton system: Application to Sundarban mangrove wetland

The paper discusses the nutrient-plankton system with effect of time delay in nutrient recycling and toxin-determined function response (TDFR). The designed model system explores the delay-induced system dynamics. We present the local stability analysis of interior equilibrium points in absence as well as in presence of time delay. Further, the direction of Hopf bifurcation is obtained. We perform the numerical computation and observe that time delay in nutrient recycling can generate the periodic solution in a stable nutrient-plankton system. Some other essential parameters, such as input concentration of nutrients and natural removal rate of nutrients, also regulate the dynamical system. The system shows Hopf and double-Hopf bifurcation in the presence of time delay. Our study shows that the delay in the nutrient recycling causes instability transition phenomenon. The delay-induced nutrient recycling and different input concentrations of nutrients can regulate the estuarine system. Finally, the stability switching is observed for delayed system.