Dynamical Behaviours of Prey-predator Fishery Model with Harvesting Affected by Toxic Substances

Abstract

In this paper we consider a harvesting model of predator-prey fishery in which the prey is directly infected by some external toxic substances. The toxic infection is indirectly transmitted to the predator during the feeding process. The model is a modied version from the classic Lotka-Volterra predator-prey model. The stability and bifurcation analyses are addressed. Numerical simulations of the model are performed and bifurcation diagrams are studied to investigate the dynamical behaviours between the predator and the prey. The eects of toxicity and harvesting on the stability of steady states found in the model are discussed.