Time lags can control algal bloom in two harmful phytoplankton–zooplankton system

A mathematical model consisting two harmful phytoplankton and zooplankton with discrete time lags in the mortality of zooplankton due to liberation of toxic substances by harmful phytoplankton has been considered. A stable co-existence of all the species has been observed for no-delay situation. Introduction of single delay in the system cause recurrent algal bloom and a threshold for the delay parameter has been estimated. Further, presence of multiple (two) delays control the oscillatory situation and can be used for termination of planktonic bloom. The analytical results as well as numerical simulations of our study lead to several threshold values for the delay parameters which play important roles in the marine ecological problems. An interesting observation is that multiple delay resolves plankton ‘paradox’ and establish a positive effect of competitive exclusion principle for stable co-existence of the species.