n this paper, our aim is mathematical analysis and numerical simulation of a
prey-predator model to describe the effect of predation between prey and predator
with nonlinear functional response. First, we develop results concerning the
boundedness, the existence and uniqueness of the solution. Furthermore, the
Lyapunov principle and the Routh–Hurwitz criterion are applied to study respectively
the local and global stability results. We also establish the Hopf-bifurcation to show
the existence of a branch of nontrivial periodic solutions. Finally, numerical
simulations have been accomplished to validate our analytical findings.

Prey-predator system; Hopf-bifurcation; Global stability; Numerical simulations