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

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 stripelike patterns.

Dispersal-induced destabilization of metapopulations and oscillatory Turing patterns in ecological networks

“…It has been shown that such instability should be generic for the two-species predator-prey models 15 (see also 16 ). Complex spatio-temporal ecological dynamics related to the Turing-Hopf 15 17 and Turing-Takens-Bogdanov 15 bifurcations has been discussed. Stationary Turing patterns have been found in realistic models describing plant-parasite 18 , plankton-fish 19 and plant-insect 20 interactions.…”