TY - JOUR
T1 - Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation
AU - Li, X.
AU - Mao, X.
AU - National Natural Science Foundation of China (Funder)
AU - Key Project of Chinese Ministry of Education (Funder)
AU - Key Laboratory for Applied Statistics of MOE (KLAS) (Funder)
PY - 2009
Y1 - 2009
N2 - In this paper, we consider a non-autonomous stochastic Lotka-Volterra competitive system dxi(t) = xi(t)[(bi(t)¡
nPj=1aij (t)xj (t))dt+¾i(t)dBi(t)], where Bi(t) (i = 1; 2; ¢ ¢ ¢ ; n) are independent standard Brownian motions.
Some dynamical properties are discussed and the su±cient conditions for the existence of global positive solutions, stochastic permanence, extinction as well as global attractivity are obtained. In addition, the limit of the average in time of the sample paths of solutions is estimated.
AB - In this paper, we consider a non-autonomous stochastic Lotka-Volterra competitive system dxi(t) = xi(t)[(bi(t)¡
nPj=1aij (t)xj (t))dt+¾i(t)dBi(t)], where Bi(t) (i = 1; 2; ¢ ¢ ¢ ; n) are independent standard Brownian motions.
Some dynamical properties are discussed and the su±cient conditions for the existence of global positive solutions, stochastic permanence, extinction as well as global attractivity are obtained. In addition, the limit of the average in time of the sample paths of solutions is estimated.
KW - brownian motion
KW - stochastic di®erential equation
KW - It^o's formula
KW - stochastic permanence
KW - global attractivity
U2 - 10.3934/dcds.2009.24.523
DO - 10.3934/dcds.2009.24.523
M3 - Article
VL - 24
SP - 523
EP - 593
JO - Discrete and Continuous Dynamical Systems - Series A
JF - Discrete and Continuous Dynamical Systems - Series A
SN - 1078-0947
IS - 2
ER -