title: Bifurcation and temporal periodic patterns in a plant-pollinator model with diffusion and time delay effects.
abstract: This paper deals with a plant-pollinator model with diffusion and time delay effects. By considering the distribution of eigenvalues of the corresponding linearized equation, we first study stability of the positive constant steady-state and existence of spatially homogeneous and spatially inhomogeneous periodic solutions are investigated. We then derive an explicit formula for determining the direction and stability of the Hopf bifurcation by applying the normal form theory and the centre manifold reduction for partial functional differential equations. Finally, we present an example and numerical simulations to illustrate the obtained theoretical results.
authors.affiliation: a School of Mathematical Sciences , Beijing Normal University , Beijing , People's Republic of China.
authors.forename: Jirong
authors.initials: J
authors.lastname: Huang
authors.affiliation: a School of Mathematical Sciences , Beijing Normal University , Beijing , People's Republic of China.
authors.forename: Zhihua
authors.initials: Z
authors.lastname: Liu
authors.affiliation: b Department of Mathematics , University of Miami , Coral Gables , FL , USA.
authors.forename: Shigui
authors.initials: S
authors.lastname: Ruan
mesh_terms: D000818:Animals; D008954:Models, Biological; D010944:Plants; D054817:Pollination; D013997:Time Factors
keywords: 35B32; 35K51; 35K57; 35Q92; 37N25; 92D25; Hopfbifurcation; Unidirectional consumer–resource interaction; delay; diffusion; stability