Open AccessBifurcation analysis and transient spatio-temporal dynamics for a diffusive plant-herbivore system with Dirichlet boundary conditions
Author(s) -
Lin Wang,
James Watmough,
Yu Fang
Publication year - 2015
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2015.12.699
Subject(s) - transient (computer programming) , dirichlet boundary condition , steady state (chemistry) , bifurcation , dirichlet distribution , boundary (topology) , stability (learning theory) , homogeneous , state space , boundary value problem , mathematics , mathematical analysis , space (punctuation) , biological system , control theory (sociology) , statistical physics , physics , computer science , nonlinear system , biology , chemistry , quantum mechanics , machine learning , operating system , statistics , control (management) , artificial intelligence
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.