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The positive coexistence of a simple food chain modelwith ratio-dependent functional response and cross-diusion is dis-cussed. Especially, when a cross-diusion is small enough, the exis-tence of positive solutions of the system concerned can be expected.The extinction conditions for all three interacting species and forone or two of three species are studied. Moreover, when a cross-diusion is suciently large, the extinction of prey species withcross-diusion interaction to predator occurs. The method em-ployed is the comparison argument for elliptic problem and xedpoint theory in a positive cone on a Banach space.
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참고문헌 (28)
참고문헌 신청
/ 1995 / Some coexistence and extinction results for a 3-species ecological system (3) : 617 ~ 626
/ 1999 / Diffusion vs cross-diffusion: an elliptic approach : 157 ~ 190
/ 2001 / Rich dynamics of a ratio-dependent one-prey two-predators model (5) : 377 ~ 396
/ 2003 / A ratio-dependent food chain model and its applications tobiological control (1) : 55 ~ 83
/ 2003 / Coexistence theorem of steady states for nonlinear self-cross diffusion systems with competitive dynamics
/ 1999 / Diffusion vs cross-diffusion: an elliptic approach : 157 ~ 190
/ 2001 / Rich dynamics of a ratio-dependent one-prey two-predators model (5) : 377 ~ 396
/ 2003 / A ratio-dependent food chain model and its applications tobiological control (1) : 55 ~ 83
/ 2003 / Coexistence theorem of steady states for nonlinear self-cross diffusion systems with competitive dynamics
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Global Existence of Solutions to the Prey-Predator System with a Single Cross-Diffusion
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ON A LOTKA-VOLTERRA TYPE SIMPLE FOOD-CHAIN MODEL
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EXISTENCE OF GLOBAL SOLUTIONS FOR A PREY-PREDATOR MODEL WITH NON-MONOTONIC FUNCTIONAL RESPONSE AND CROSS-DIFFUSION
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UNIQUENESS OF POSITIVE SOLUTIONS FOR PREDATOR-PREY INTERACTING SYSTEMS WITH NONLINEAR DIFFUSION RATES
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Dynamic analysis of a modified stochastic predator-prey system with general ratio-dependent functional response
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EXISTENCE OF NON-CONSTANT POSITIVE SOLUTIONS FOR A RATIO-DEPENDENT PREDATOR-PREY SYSTEM WITH DISEASE IN THE PREY
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MATHEMATICAL ANALYSIS OF A NONDIMENSIONAL THREE SPECIES FOOD CHAIN MODEL WITH RATIO DEPENDENCE
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STATIONARY PATTERNS FOR A PREDATOR-PREY MODEL WITH HOLLING TYPE Ⅲ RESPONSE FUNCTION AND CROSS-DIFFUSION
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W½-estimates on the prey-predator systems with cross-diffusions and functional responses
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POSITIVE SOLUTIONS FOR CERTAIN ELLIPTIC SYSTEMS WITH THREE SPECIES INVOLVING SYMBIOTIC INTERACTIONS
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Controlling extinction of species in food chain
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PATTERN FORMATION FOR A RATIO-DEPENDENT PREDATOR-PREY MODEL WITH CROSS DIFFUSION
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Global asymptotic stability of positive steady states of an n-dimensional ratio-dependent predator-prey system with diffusion
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Periodic solutions of a discrete time non-autonomous ratio-dependent predator-prey system with control
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PHASE ANALYSIS FOR THE PREDATOR-PREY SYSTEMS WITH PREY DENSITY DEPENDENT RESPONSE
순수 및 응용수학
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TURING INSTABILITY IN A PREDATOR-PREY MODEL IN PATCHY SPACE WITH SELF AND CROSS DIFFUSION
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Comparative Analysis of Large Genome in Cross-species
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2003 .01
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INSTABILITY IN A PREDATOR-PREY MODEL WITH DIFFUSION
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Permanence of a Three-species Food Chain System with Impulsive Perturbations
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2008 .01
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ALTERNATIVE PROOF OF EXISTENCE THEOREM FOR CERTAIN COMPETITION MODELS
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