Open AccessGlobal dynamics of a di usive single species model with periodic delay
Author(s) -
Yan Zhang,
San Yang Liu,
Zhen Guo Bai
Publication year - 2019
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.2019114
Subject(s) - bounded function , homogeneous , domain (mathematical analysis) , boundary (topology) , population , population model , neumann boundary condition , periodic boundary conditions , mathematics , oscillation (cell signaling) , dynamics (music) , statistical physics , boundary value problem , mathematical analysis , physics , biology , demography , sociology , acoustics , genetics
The growth of the species population is greatly influenced by seasonally varying environments. By regarding the maturation age of the species as a periodic developmental process, we propose a time periodic and diffusive model in bounded domain. To analyze this model with periodic delay, we first define the basic reproduction ratio R ₀ of the spatially homogeneous model and then show that the species population will be extinct when R ₀≤1 while remains persistent and tends to periodic oscillation if R ₀>1. Finally, combining the comparison principle with the fact that solutions of the spatially homogeneous model are also solutions of our model subject to Neumann boundary condition, we establish the global dynamics of a threshold type for PDE model in terms of R ₀.