Poster Session

Bifurcation and Stability Analysis of a Holling type II Predator-Prey Model with Omnivores

Sambath Muniyagounder
Periyar University
India
Co-Author(s):    C. GOKILA
Abstract:
This paper consider a predator prey model with omnivore population and Holling type II response. First, we have studied the boundedness of the 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 formula which determine the direction of bifurcating periodic solutions are derived. Some numerical simulations are carrying out, to check our theoretical results.