POSITIVE SOLUTIONS FOR A PREDATOR-PREY INTERACTION MODEL WITH HOLLING-TYPE FUNCTIONAL RESPONSE AND DIFFUSION

We deal with a predator-prey interaction model with Holling-type monotonic functional response and diffusion and which is endowed with a second homogeneous boundary condition. Via spectrum analysis and bifurcation theory, we investigate the local and global bifurcation solutions of the model which e...

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Bibliographic Details
Published inTaiwanese journal of mathematics Vol. 15; no. 5; pp. 2013 - 2034
Main Authors Jia, Yunfeng, Wu, Jianhua, Xu, Hong-Kun
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.10.2011
Subjects
Bifurcation theory
Ecological modeling
Eigenvalues
Functional responses
Mathematical constants
Ordinary differential equations
Population ecology
Predator prey relationships
Predators
Steady state theory
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Summary:We deal with a predator-prey interaction model with Holling-type monotonic functional response and diffusion and which is endowed with a second homogeneous boundary condition. Via spectrum analysis and bifurcation theory, we investigate the local and global bifurcation solutions of the model which emanate from a positive constant solution by taking the growth rate as a bifurcation parameter. Basing on the fixed point index theory, we prove the existence of positive steady-state solutions of the model. 2010Mathematics Subject Classification: Primary 92D25; Secondary 93C20, 35K57. Key words and phrases: Predator-prey model, Positive solution, Functional response, Bifurcation theory, Fixed point index theory, Stability, Crandall-Rabinowitz's bifurcation theorem.
ISSN:1027-5487
2224-6851
DOI:10.11650/twjm/1500406420