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

AM > Vol.2 No.12, December 2011

Applied Mathematics

Volume 2, Issue 12 (December 2011)

ISSN Print: 2152-7385 ISSN Online: 2152-7393

Google-based Impact Factor: 0.58 Citations

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

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DOI: 10.4236/am.2011.212213 4,411 Downloads 8,177 Views Citations

Author(s)

Dawit Melese, Sunita Gakkhar

Affiliation(s)

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

Share and Cite:

D. Melese and S. Gakkhar, "Pattern Formation in Tri-Trophic Ratio-Dependent Food Chain Model," Applied Mathematics, Vol. 2 No. 12, 2011, pp. 1507-1514. doi: 10.4236/am.2011.212213.

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