A system of two competitive prey species in presence of predator under the in uence of toxic substances

Abstract

In this article, a two prey - one predator model has been studied where two prey species are competitive in nature and also uses toxic substances to each other for own existence. Biologically well posedness of the model system has been shown through positivity and boundedness of solutions. Existence criterion and stability analysis of the non-negative equilibrium points have been discussed. The sucient
conditions for existence of Hopf bifurcation and stability switches induced by delay are investigated. The direction and the stability criteria of the bifurcating periodic solutions are determined with the help of the normal form theory and the center manifold theorem. Numerical simulations are performed to illustrate
the theoretical analysis results.