Positive coexistence for a simple food chain model with Ratio-dependent functional response and cross-diffusion
Commun. Korean Math. Soc. 2006 Vol. 21, No. 4, 701-717
Published online December 1, 2006
Wonlyul Ko, Inkyung Ahn
Korea University, Korea University
Abstract : The positive coexistence of a simple food chain model with ratio-dependent functional response and cross-diffusion is discussed. Especially, when a cross-diffusion is small enough, the existence of positive solutions of the system concerned can be expected. The extinction conditions for all three interacting species and for one or two of three species are studied. Moreover, when a cross-diffusion is sufficiently large, the extinction of prey species with cross-diffusion interaction to predator occurs. The method employed is the comparison argument for elliptic problem and fixed point theory in a positive cone on a Banach space.
Keywords : positive solution, ratio-dependent, fixed point index, upper/lower solution, cross-diffusion
MSC numbers : 35J60, 35Q80
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