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POSITIVE COEXISTENCE FOR A SIMPLE FOOD CHAIN MODEL WITH RATIO-DEPENDENT FUNCTIONAL RESPONSE AND CROSS-DIFFUSION
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 Title & Authors
POSITIVE COEXISTENCE FOR A SIMPLE FOOD CHAIN MODEL WITH RATIO-DEPENDENT FUNCTIONAL RESPONSE AND CROSS-DIFFUSION
Ko, Won-Lyul; Ahn, In-Kyung;
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 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;
 Language
English
 Cited by
1.
[ W12 ]-ESTIMATES ON THE PREY-PREDATOR SYSTEMS WITH CROSS-DIFFUSIONS AND FUNCTIONAL RESPONSES,;

대한수학회논문집, 2008. vol.23. 2, pp.211-227 crossref(new window)
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