Bifurcation and temporal periodic patterns in a plant–pollinator model with diffusion and time delay effects

Journal of Biological Dynamics

Jirong Huang¹  Zhihua Liu¹  Shigui Ruan² 

[1] Beijing Normal University;University of Miami;

关键词: Unidirectional consumer–resource interaction;    diffusion;    delay;    stability;    Hopfbifurcation;   

DOI  :  10.1080/17513758.2016.1181802

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown