1Assistant Professor, Department of Applied Mathematics and Computational Sciences, PSG College of Technology, Coimbatore-641 004
2UGC-BSR Faculty Fellow, Department of Mathematics, Bharathiar University, Coimbatore-641 046, India, kb.maths.bu@gmail.com
*Corresponding author E-mail: sivamaths007@gmail.com
2010 Mathematics Subject Classification: 92D25, 70K50, 35B35
In this paper, we examine a diffusive ratio dependent predator-prey model with prey refuge subject to Neumann boundary condition. We discuss the stability of the positive equilibrium and the existence of spatially homogeneous and inhomogeneous periodic solutions through distribution of the eigenvalues. The direction and stability of Hopf bifurcation are determined by the normal form theory and the center manifold theory. Finally numerical simulations are given to validate our analytical results.
Stability and bifurcation analysis, Diffusive Holling Tanner, predator-prey model, prey refuge
