Taiwanese Journal of Mathematics


Yunfeng Jia, Jianhua Wu, and Hong-Kun Xu

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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.

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Taiwanese J. Math., Volume 15, Number 5 (2011), 2013-2034.

First available in Project Euclid: 18 July 2017

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Zentralblatt MATH identifier

Primary: 92D25: Population dynamics (general)
Secondary: 93C20: Systems governed by partial differential equations 35K57: Reaction-diffusion equations

predator-prey model positive solution functional response bifurcation theory fixed point index theory stability Crandall-Rabinowitz's bifurcation theorem


Jia, Yunfeng; Wu, Jianhua; Xu, Hong-Kun. POSITIVE SOLUTIONS FOR A PREDATOR-PREY INTERACTION MODEL WITH HOLLING-TYPE FUNCTIONAL RESPONSE AND DIFFUSION. Taiwanese J. Math. 15 (2011), no. 5, 2013--2034. doi:10.11650/twjm/1500406420. https://projecteuclid.org/euclid.twjm/1500406420

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