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J Biol Dyn

Title:		Transient spatio-temporal dynamics of a diffusive plant-herbivore system with Neumann boundary conditions
Author(s):		Yu F; Wang L; Watmough J;
Address:		"a Department of Mathematics and Statistics , University of New Brunswick , Fredericton , Canada"
Journal Title:		J Biol Dyn
Year:		2016
Volume:		10
Issue:		1
Page Number:		477 - 500
DOI:		10.1080/17513758.2016.1218961
ISSN/ISBN:		1751-3766 (Electronic) 1751-3758 (Linking)
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"
Keywords:		"Animals Computer Simulation Ecosystem *Herbivory *Models, Biological Population Dynamics Hopf bifurcation Neumann boundary condition Plant-herbivore interaction Primary: 35B32, 35B35 Secondary: 92B05 steady-state bifurcation transient dynamics;"
Notes:		"MedlineYu, Fang Wang, Lin Watmough, James eng England 2016/08/31 J Biol Dyn. 2016 Dec; 10(1):477-500. doi: 10.1080/17513758.2016.1218961"