Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 78, Issue 1, Pages 191-203Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2019.02.023
Keywords
Predator-prey model; Prey-taxis; Reaction-diffusive system; Global bifurcation; A priori estimates
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Funding
- Project of Scientific Research on Introducing Talents to Guizhou University of Finance and Economics [2018YJ17]
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In this paper, a general reaction-diffusive predator-prey system with prey-taxis subject to the homogeneous Neumann boundary condition is considered. Firstly, we investigate the local stability of the unique positive equilibrium by analyzing the characteristic equation and study a priori estimates of positive solutions by the iterative technique. And then, choosing the prey-tactic sensitivity coefficient as bifurcation parameter, we proved that a branch of nonconstant solutions can bifurcate from the unique positive equilibrium when the prey-tactic sensitivity is repulsive. Moreover, we find the stable bifurcating solutions near the bifurcation point by the spectrum theory under some suitable conditions. Our results show that prey-taxis can destabilize the uniform equilibrium and yields the occurrence of spatial patterns. (C) 2019 Elsevier Ltd. All rights reserved.
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