Selective harvesting of two competing fish species in the presence of toxicity with time delay

In this paper, we have considered a two competing fish species with the delay due to gestation, each of which obeys the law of logistic growth and releases a substance toxic to the other. We also consider the selective harvesting of fishes above a certain age or size by incorporating a time delay in the harvesting term. The dynamical behavior of the exploited system is examined in the presence and absence of delay. Boundedness, local and global stabilities are addressed. The possibility of the existence of a dynamic equilibrium and the optimal harvesting policy is studied in the absence of delay. It is shown that the time delay can cause a stable equilibrium to become unstable and even a switching of stabilities. Extensive numerical simulations are performed using analytical results for a hypothetical set of parameter values.