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The present paper deals with the mathematical analysis of a prey–predator model where the prey population is assumed to live in two distinct habitats and the predator consumes prey from both these habitats with a switching tendency. The dynamical behavior of the system is investigated from the point of view of stability and bifurcation aspects. It has been found that the mortality rate of the predator plays an important role in controlling the system dynamics. Finally, a detailed study of the Hopf-bifurcating solutions is carried out and the criteria for subcritical and supercritical Hopf-bifurcation derived. Numerical simulations are performed in support of analytical results.

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.