Antipredator behaviour in a predator-prey system in presence of a competitor

Abstract

This paper introduces a prey-predator system in the presence of a competitor for the prey and anti-predator behaviour such that the adult preys can attack vulnerable predators. Mathematical analysis shows that increase the amount of antipredator behaviour rate can increase prey density and decrease competitor density. As far as the predator species is concerned, when the assumption a12a21 ≤ a11a22 holds, increasing the amount of antipredator behaviour can decrease the predator density whereas the opposite holds if the assumption is reversed. Local, global stability and bifurcation study as well as stability of the limit cycle is analyzed. Here for specific parametric choice we obtain chaotic behaviour of our system in a simple Lotka Volterra model. Numerical simulation study with some hypothetical data is also performed.This paper introduces a prey-predator system in the presence of a competitor for the prey and anti-predator behaviour such that the adult preys can attack vulnerable predators. Mathematical analysis shows that increase the amount of antipredator behaviour rate can increase prey density and decrease competitor density. As far as the predator species is concerned, when the assumption a12a21 ≤ a11a22 holds, increasing the amount of antipredator behaviour can decrease the predator density whereas the opposite holds if the assumption is reversed. Local, global stability and bifurcation study as well as stability of the limit cycle is analyzed. Here for specific parametric choice we obtain chaotic behaviour of our system in a simple Lotka Volterra model. Numerical simulation study with some hypothetical data is also performed.