Qualitative analysis of additional food provided predator–prey system with anti-predator behaviour in prey

Abstract

Predator–prey interactions are the most common phenomena in the natural population, which are widely exploited for control of economically damaging pest species in an eco-friendly manner. It is proven that the pest adopts several mechanisms for overcoming the predation pressure. Two such techniques which are not well studied in the literature are group defence, anti-predator behaviour in prey. Anti-predator behaviour of prey is a counterattacking technique, in which adult prey attacks the juvenile predators to reduce the future predation pressure. From the existing experimental studies, it is observed that the anti-predator behaviour of the pest can have adverse effects on the biological control programmes. One of the ways to overcome the loss due to anti-predator behaviour is to cater the predators with some alternative food. In this current work, we have investigated this aspect in a dynamical system framework. This study uncovers many fascinating phenomena. It is found that the considered system displays rich dynamics and demonstrates various bifurcations such as saddle-node bifurcation, (supercritical and subcritical) Hopf bifurcation, homoclinic bifurcation and a Bogdanov–Takens bifurcation of co-dimension 2 are studied. Treating the anti-predator behaviour in prey as one of the control parameters, and by characterising the additional food supplied to the predators, the strategies for achieving the successful biological control are derived.