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Published in:
2012 | OriginalPaper | Chapter
A Stochastic Lotka-Volterra System and Its Asymptotic Behavior
Authors : Liangjian Hu, Juanjuan Zhao
Published in: System Simulation and Scientific Computing
Publisher: Springer Berlin Heidelberg
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In this paper, we investigate a new Lotka-Volterra system
$$ dx(t)=\textrm{diag}(x_1(t),...,x_n(t))[(b+Ax(t))dt+\sigma x(t)^{p}dw(t))] ,\nonumber $$
where
w
(
t
) is a standard Brownian motion, and
x
p
is defined as
$(x_{1}^{p},...,x_{n}^{p})^{T}$
. Population systems perturbed by the white noise have recently been studied by many authors in case of
p
= 0 and
p
= 1. The aim here is to find out what happens when
$p\ge\frac{1}{2}$
. This paper shows environmental Brownian noise suppresses explosions in this system. In addition, we examine the asymptotic behavior of the system.