Effects of Delay and Seasonality on Toxin Producing Phytoplankton–zooplankton System

A dynamical model for toxin producing phytoplankton and zooplankton has been formulated and analyzed. Due to gestation of prey, a discrete time delay is incorporated in the predator dynamics. The stability of the delay model is discussed and Hopf bifurcation to a periodic orbit is established. Stability and direction of bifurcating periodic orbits are investigated using normal form theory and center manifold arguments. Global existence of periodic orbits is also established. To substantiate analytical findings, numerical simulations are performed. The system shows rich dynamic behavior including chaos and limit cycles. The influence of seasonality in intrinsic growth parameter of the phytoplankton population is also investigated. Seasonality leads to complexity in the system.