Pattern Formation in Tri-Trophic Ratio-Dependent Food Chain Model

Dawit Melese, Sunita Gakkhar

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DOI: 10.4236/am.2011.212213                

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.

Keywords

Reaction-Diffusion Equations, Hopf Bifurcation, Turing Instability, Turing Pattern, Food Chain

Conflicts of Interest

The authors declare no conflicts of interest.

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