Stability and bifurcation in a non-kolmogorov type prey-predator system with time delay

The purpose of this paper is to study a non-Kolmogrov type prey-predator system. First, we investigate the linear stability of the model by analyzing the associated characteristic equation of the linearized system. Second, we show that the system exhibits the Hopf bifurcation. The stability and direction of the Hopf bifurcation are determined by applying the norm form theory and center manifold theorem. Finally, numerical simulations are performed to illustrate the obtained results.