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Mathematical Biosciences and Engineering

2015, Volume 12, Issue 4: 699-715. doi: 10.3934/mbe.2015.12.699
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Bifurcation analysis and transient spatio-temporal dynamics for a diffusive plant-herbivore system with Dirichlet boundary conditions

  • 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
  • Published: 01 April 2015

  • MSC : Primary: 35B32, 35B35; Secondary: 92B05.

  • 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

    Related Papers:

  • 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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  • © 2015 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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