Journal
BULLETIN OF MATHEMATICAL BIOLOGY
Volume 79, Issue 3, Pages 560-593Publisher
SPRINGER
DOI: 10.1007/s11538-017-0245-x
Keywords
Reaction-diffusion predator-prey system; Beddington-DeAngelis functional response; Stability; Turing pattern; Weakly nonlinear analysis
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Funding
- National Science Foundation [DMS-1412454]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1412454] Funding Source: National Science Foundation
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We study a diffusive predator-prey model describing the interactions of small fishes and their resource base (small invertebrates) in the fluctuating freshwater marsh landscapes of the Florida Everglades. The spatial model is described by a reaction-diffusion system with Beddington-DeAngelis functional response. Uniform bound, local and global asymptotic stability of the steady state of the PDE model under the no-flux boundary conditions are discussed in details. Sufficient conditions on the Turing (diffusion-driven) instability which induces spatial patterns in the model are derived via linear analysis. Existence of one-dimensional and two-dimensional spatial Turing patterns, including rhombic and hexagonal patterns, are established by weakly nonlinear analyses. These results provide theoretical explanations and numerical simulations of spatial dynamical behaviors of the wetland ecosystems of the Florida Everglades.
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