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http://dx.doi.org/10.4134/CKMS.2006.21.4.701

POSITIVE COEXISTENCE FOR A SIMPLE FOOD CHAIN MODEL WITH RATIO-DEPENDENT FUNCTIONAL RESPONSE AND CROSS-DIFFUSION  

Ko, Won-Lyul (Department of Mathematics Korea University)
Ahn, In-Kyung (Department of Mathematics Korea University)
Publication Information
Communications of the Korean Mathematical Society / v.21, no.4, 2006 , pp. 701-717 More about this Journal
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;
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