A 3-dimensional nutrient-prey-predator model with intratrophic predation is proposed and studied. Some elementary properties such as invariance of nonnegativity, boundedness and dissipativity of the system are presented. The purpose of this chapter is to study the existence and stability of equilibria along with the effects of intratrophic predation towards the positions and stability of those equilibria of the system. We also investigate the occurrence of Hopf bifurcation. In the case when there is no presence of predator organisms, intratrophic predation may not give impact on the stability of equilibria of the system. We also analysed global stability of the equilibrium point. A suitable Lyapunov function is defined for global stability analysis and some results of persistence analysis are presented for the existence of positive interior equilibrium point. Besides that, Hopf bifurcation analysis of the system are demonstrated.
Part of the book: Complexity in Biological and Physical Systems