In this paper, we study a diffusive plant-herbivore system with homogeneous and nonhomogeneous Dirichlet boundary conditions.Stability of spatially homogeneous steady states is established. We also derive conditions ensuring the occurrence of Hopfbifurcation and steady state bifurcation. Interesting transient spatio-temporal behaviors including oscillations in one or both of space and time are observed through numerical simulations.
Citation: Lin Wang, James Watmough, Fang Yu. Bifurcation analysis and transient spatio-temporal dynamics for a diffusive plant-herbivore system with Dirichlet boundary conditions[J]. Mathematical Biosciences and Engineering, 2015, 12(4): 699-715. doi: 10.3934/mbe.2015.12.699
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Abstract
In this paper, we study a diffusive plant-herbivore system with homogeneous and nonhomogeneous Dirichlet boundary conditions.Stability of spatially homogeneous steady states is established. We also derive conditions ensuring the occurrence of Hopfbifurcation and steady state bifurcation. Interesting transient spatio-temporal behaviors including oscillations in one or both of space and time are observed through numerical simulations.
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