TITLE:
Pattern Formation in Tri-Trophic Ratio-Dependent Food Chain Model
AUTHORS:
Dawit Melese, Sunita Gakkhar
KEYWORDS:
Reaction-Diffusion Equations, Hopf Bifurcation, Turing Instability, Turing Pattern, Food Chain
JOURNAL NAME:
Applied Mathematics,
Vol.2 No.12,
December
27,
2011
ABSTRACT: In this paper, a spatial tri-trophic food chain model with ratio-dependent Michaelis-Menten type functional response under homogeneous Neumann boundary conditions is studied. Conditions for Hopf and Turing bifurcation are derived. Sufficient conditions for the emergence of spatial patterns are obtained. The results of numerical simulations reveal the formation of labyrinth patterns and the coexistence of spotted and stripe-like patterns.