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S. B. Hsu, T. W. Hwang and Y. Kuang, “A Ratio-Dependent Food Chain Model and Its Applications to Biological Control,” Mathematical Biosciences, Vol. 181, No. 1, 2003, pp. 55-83. doi:10.1016/S0025-5564(02)00127-X

has been cited by the following article:

• 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.