Linear and Weakly Nonlinear Stability Analyses of Turing Patterns for Diffusive Predator–Prey Systems in Freshwater Marsh Landscapes

Li Zhang, Fan Zhang, Shigui Ruan

Research output: Contribution to journalArticle

2 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)560-593
Number of pages34
JournalBulletin of Mathematical Biology
Volume79
Issue number3
DOIs
StatePublished - Mar 1 2017

Fingerprint

Turing Patterns
Wetlands
Predator-prey System
Nonlinear Stability
Spatial Pattern
Fresh Water
marshes
marsh
Spatial Behavior
Beddington-DeAngelis Functional Response
Local Asymptotic Stability
Uniform Bound
Predator-prey Model
Spatial Model
Global Asymptotic Stability
Turing
Invertebrates
Fish
Reaction-diffusion System
Ecosystem

Keywords

  • Beddington–DeAngelis functional response
  • Reaction–diffusion predator–prey system
  • Stability
  • Turing pattern
  • Weakly nonlinear analysis

ASJC Scopus subject areas

  • Neuroscience(all)
  • Immunology
  • Mathematics(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Pharmacology
  • Environmental Science(all)
  • Agricultural and Biological Sciences(all)
  • Computational Theory and Mathematics

Cite this

Linear and Weakly Nonlinear Stability Analyses of Turing Patterns for Diffusive Predator–Prey Systems in Freshwater Marsh Landscapes. / Zhang, Li; Zhang, Fan; Ruan, Shigui.

In: Bulletin of Mathematical Biology, Vol. 79, No. 3, 01.03.2017, p. 560-593.

Research output: Contribution to journalArticle

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