title: Transient spatio-temporal dynamics of a diffusive plant-herbivore system with Neumann boundary conditions.
abstract: In many existing predator-prey or plant-herbivore models, the numerical response is assumed to be proportional to the functional response. In this paper, without such an assumption, we consider a diffusive plant-herbivore system with Neumann boundary conditions. Besides stability of spatially homogeneous steady states, we also derive conditions for the occurrence of Hopf bifurcation and steady-state bifurcation and provide geometrical methods to locate the bifurcation values. We numerically explore the complex transient spatio-temporal behaviours induced by these bifurcations. A large variety of different types of transient behaviours including oscillations in one or both of space and time are observed.
authors: a Department of Mathematics and Statistics , University of New Brunswick , Fredericton , Canada.
authors: Fang
authors: F
authors: Yu
authors: a Department of Mathematics and Statistics , University of New Brunswick , Fredericton , Canada.
authors: Lin
authors: L
authors: Wang
authors: a Department of Mathematics and Statistics , University of New Brunswick , Fredericton , Canada.
authors: James
authors: J
authors: Watmough
mesh_terms: D000818:Animals; D003198:Computer Simulation; D017753:Ecosystem; D060434:Herbivory; D008954:Models, Biological; D011157:Population Dynamics
keywords: Hopf bifurcation; Neumann boundary condition; Plant–herbivore interaction; Primary: 35B32, 35B35; Secondary: 92B05; steady-state bifurcation; transient dynamics