The Influence of Density Dependent Death Rate of Predator Species to the Lotka-Volterra Predator Prey System with Fear Effect

Abstract

A Lotka-Volterra predator prey system incorporating fear effect of the prey species and density dependent death rate of predator species is proposed and studied in this paper. Local and global stability property of the equilibria are investigated. Our study shows that the density dependent death rate of predator species has no influence to the persistent or extinction property of the system. However, with the increasing of the density dependent death rate, the final density of the predator species is decreasing and the final density of the prey species is increasing. Hence, the increasing of the the density dependent death rate enhance the possibility of the extinction of the predator specie. Numeric simulations show that too high density dependent death rate and too high fear effect of prey species may lead to the extinction of the predator species.