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Volume 10, Number 1, 2020, Pages 165-177                                                                DOI:10.11948/20190097
Spatial pattern formations in diffusive predator-prey systems with non-homogeneous Dirichlet boundary conditions
Yingwei Song,Tie Zhang
Keywords:Reaction, diffusion, predator-prey, stability, bifurcation.
      A reaction-diffusion predator-prey system with non-homogeneous Dirichlet boundary conditions describes the persistence of predator and prey species on the boundary. Compared with homogeneous Neumann boundary conditions, the former conditions may prompt or prevent the spatial patterns produced through diffusion-induced instability. The spatial pattern formation induced by non-homogeneous Dirichlet boundary conditions is characterized by the Turing type linear instability of homogeneous state and bifurcation theory. Furthermore, transient spatiotemporal behaviors are observed through numerical simulations.
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