TY - JOUR
T1 - Asymptotic behaviour of the stochastic Lotka-Volterra model
AU - Mao, Xuerong
AU - Sabanis, Sotirios
AU - Renshaw, Eric
PY - 2003/11/1
Y1 - 2003/11/1
N2 - This paper examines the asymptotic behaviour of the stochastic extension of a fundamentally important population process, namely the Lotka-Volterra model. The stochastic version of this process appears to have far more intriguing properties than its deterministic counterpart. Indeed, the fact that a potential deterministic population explosion can be prevented by the presence of even a tiny amount of environmental noise shows the high level of difference which exists between these two representations.
AB - This paper examines the asymptotic behaviour of the stochastic extension of a fundamentally important population process, namely the Lotka-Volterra model. The stochastic version of this process appears to have far more intriguing properties than its deterministic counterpart. Indeed, the fact that a potential deterministic population explosion can be prevented by the presence of even a tiny amount of environmental noise shows the high level of difference which exists between these two representations.
KW - asymptotic behaviour
KW - Brownian motion
KW - Lotka-Volterra model
KW - moment boundedness
KW - stochastic differential equation
UR - http://www.scopus.com/inward/record.url?scp=0242676984&partnerID=8YFLogxK
UR - http://www.sciencedirect.com/science/article/pii/S0022247X03005390
U2 - 10.1016/S0022-247X(03)00539-0
DO - 10.1016/S0022-247X(03)00539-0
M3 - Article
AN - SCOPUS:0242676984
SN - 0022-247X
VL - 287
SP - 141
EP - 156
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -