Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 251, Issue 4-5, Pages 1276-1304Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2011.03.004
Keywords
Reaction-diffusion system; Predator-prey; Bifurcation; Strong Allee effect; Spatiotemporal patterns
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Funding
- National Natural Science Foundation of China [11031002, 11071051]
- National Science Foundation of US [DMS-1022648]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1022648] Funding Source: National Science Foundation
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The dynamics of a reaction-diffusion predator-prey system with strong Allee effect in the prey population is considered. Nonexistence of nonconstant positive steady state solutions are shown to identify the ranges of parameters of spatial pattern formation. Bifurcations of spatially homogeneous and nonhomogeneous periodic solutions as well as nonconstant steady state solutions are studied. These results show that the impact of the Allee effect essentially increases the system spatiotemporal complexity. (C) 2011 Elsevier Inc. All rights reserved.
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