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Mathematical Biosciences and Engineering (MBE)
 

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

Pages: 699 - 715, Volume 12, Issue 4, August 2015      doi:10.3934/mbe.2015.12.699

 
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Lin Wang - Department of Mathematics and Statistics, University of New Brunswick, Fredericton, NB, E3B 5A3, Canada (email)
James Watmough - Department of Mathematics and Statistics, University of New Brunswick, Fredericton, New Brunswick, E3B 5A3, Canada (email)
Fang Yu - Department of Mathematics and Statistics, University of New Brunswick, Fredericton, New Brunswick, E3B 5A3, Canada (email)

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 Hopf bifurcation and steady state bifurcation. Interesting transient spatio-temporal behaviors including oscillations in one or both of space and time are observed through numerical simulations.

Keywords:  Plant-herbivore interaction, diffusion, Hopf bifurcation, steady state bifurcation, transient dynamics.
Mathematics Subject Classification:  Primary: 35B32, 35B35; Secondary: 92B05.

Received: March 2014;      Accepted: December 2014;      Available Online: April 2015.

 References