Hall 123

Stability, bifurcation and pattern formation of a diffusive predator-prey model

M. Sambath

Department of Mathematics, Bharathiar University, Coimbatore 641 046, India

The research reported in this presentation deals with the stability, Hopf bifurcation and pattern formation of diffusive predator-prey model. First, we study the local stability and Hopf bifurcation at the positive equilibrium in the absence of diffusion. Further we discuss the diffusion driven instability, Hopf bifurcation for corresponding diffusion system with zero flux boundary condition and Turing instability region. We also study the spatial patterns of predator-prey model with cross diffusion. Our results reveal that cross diffusion can induce rich patterns, such as spotted, striped, spatial chaos and labyrinthine patterns, which may help us to understand the dynamics of the real ecosystems better. Our theoretical findings are supported by numerical simulations.