title: Linear and Weakly Nonlinear Stability Analyses of Turing Patterns for Diffusive Predator-Prey Systems in Freshwater Marsh Landscapes.
abstract: 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.
authors.affiliation: School of Mathematics and Statistics, Xidian University, Xi'an, 710071, Shaanxi, China.
authors.forename: Li
authors.initials: L
authors.lastname: Zhang
authors.affiliation: Department of Mathematics, University of Miami, Coral Gables, FL, 33146, USA.
authors.forename: Fan
authors.initials: F
authors.lastname: Zhang
authors.affiliation: Department of Mathematics, University of Miami, Coral Gables, FL, 33146, USA. ruan@math.miami.edu.
authors.forename: Shigui
authors.identifier: 0000-0002-6348-8205
authors.initials: S
authors.lastname: Ruan
mesh_terms: D000818:Animals; D003198:Computer Simulation; D005399:Fishes; D005431:Florida; D020387:Food Chain; D005618:Fresh Water; D055641:Mathematical Concepts; D008954:Models, Biological; D017711:Nonlinear Dynamics; D011235:Predatory Behavior; D053833:Wetlands
keywords: Beddington–DeAngelis functional response; Reaction–diffusion predator–prey system; Stability; Turing pattern; Weakly nonlinear analysis