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

Article Contents

2015, Volume 12, Issue 4: 699-715. Doi: 10.3934/mbe.2015.12.699 open access

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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

Received: February 28, 2014

Revised: November 30, 2014

Published: March 2015

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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 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.

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Mathematics Subject Classification: Primary: 35B32, 35B35; Secondary: 92B05.

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