Abstract
This paper considers a prey predator model with omnivore population and Holling type II response. First, we have studied the boundedness of the model system. The local and global stability of the equilibrium is investigated by analyzing the eigenvalues and constructing the appropriate Lyapunov functions respectively. The persistence of positive equilibrium is also discussed. The existence of Hopf bifurcation is investigated by analyzing the distribution of eigenvalues at the positive equilibrium point. By using the normal form theory and explicit formulae which determine the direction of bifurcating periodic solutions are derived. Some numerical simulations are carrying out, to check our theoretical results.
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