Bifurcation analysis and transient spatio-temporal dynamics for a diffusive plant-herbivore system with Dirichlet boundary conditions

Lin Wang; James Watmough; Fang Yu

doi:10.3934/mbe.2015.12.699

Mathematical Biosciences and Engineering, 2015, 12(4): 699-715. doi: 10.3934/mbe.2015.12.699. Primary: 35B32, 35B35; Secondary: 92B05.

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Bifurcation analysis and transient spatio-temporal dynamics for a diffusive plant-herbivore system with Dirichlet boundary conditions

Lin Wang, James Watmough, Fang Yu

1. Department of Mathematics and Statistics, University of New Brunswick, Fredericton, NB, E3B 5A3
2. Department of Mathematics and Statistics, University of New Brunswick, Fredericton, New Brunswick, E3B 5A3

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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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Keywords: Plant-herbivore interaction; transient dynamics.; Hopf bifurcation; diffusion; steady state bifurcation

Citation: Lin Wang, James Watmough, Fang Yu. Bifurcation analysis and transient spatio-temporal dynamics for a diffusive plant-herbivore system with Dirichlet boundary conditions. Mathematical Biosciences and Engineering, 2015, 12(4): 699-715. doi: 10.3934/mbe.2015.12.699

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Copyright Info: 2015, Lin Wang, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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