Geodesic
Persistence and extinction for a stochastic logistic model with infinite delay
Electronic journal of differential equations, Tome 2013 (2013)
This article, studies a stochastic logistic model with infinite delay. Using a phase space, we establish sufficient conditions for the extinction, nonpersistence in the mean, weak persistence, and stochastic permanence. A threshold between weak persistence and extinction is obtained. Our results state that different types of environmental noises have different effects on the persistence and extinction, and that the delay has no impact on the persistence and extinction for the stochastic model in the autonomous case. Numerical simulations illustrate the theoretical results.
Classification : 64H40, 92D25, 60H10, 34K50
Keywords: white noise, persistence, extinction, delay 
@article{EJDE_2013__2013__a55,
     author = {Lu,  Chun and Ding,  Xiaohua},
     title = {Persistence and extinction for a stochastic logistic model with infinite delay},
     journal = {Electronic journal of differential equations},
     year = {2013},
     volume = {2013},
     zbl = {1297.60039},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a55/}
}
TY  - JOUR
AU  - Lu,  Chun
AU  - Ding,  Xiaohua
TI  - Persistence and extinction for a stochastic logistic model with infinite delay
JO  - Electronic journal of differential equations
PY  - 2013
VL  - 2013
UR  - http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a55/
LA  - en
ID  - EJDE_2013__2013__a55
ER  - 
%0 Journal Article
%A Lu,  Chun
%A Ding,  Xiaohua
%T Persistence and extinction for a stochastic logistic model with infinite delay
%J Electronic journal of differential equations
%D 2013
%V 2013
%U http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a55/
%G en
%F EJDE_2013__2013__a55
Lu,  Chun; Ding,  Xiaohua. Persistence and extinction for a stochastic logistic model with infinite delay. Electronic journal of differential equations, Tome 2013 (2013). http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a55/