Stationary distribution of stochastic population systems

Research output: Contribution to journalArticle

74 Citations (Scopus)

Abstract

In this paper we consider the stochastic differential equation (SDE) population model dx(t) = diag(x1(t), . . . , xn(t))[(b + Ax(t))dt + σdB(t)] for n interacting species. The main aim is to study the stationary distribution of the solution. It is known (see e.g. Bahar and Mao (2004) [2] and Mao (2005) [6]) if the noise intensity is sufficiently large then the population may become extinct with probability one. Our main aim here is to find out what happens if the noise is relatively small. In this paper we will show the existence of a unique stationary distribution. We will then develop a useful method to compute the mean and variance of the stationary distribution. Computer simulations will be used to illustrate our theory.
LanguageEnglish
Pages398-405
Number of pages8
JournalSystems and Control Letters
Volume60
Issue number6
Early online date7 Apr 2011
DOIs
Publication statusPublished - Jun 2011

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Differential equations
Computer simulation

Keywords

  • Brownian motion
  • stochastic differential equation
  • Ito's formula
  • stationary distribution

Cite this

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Stationary distribution of stochastic population systems. / Mao, Xuerong.

In: Systems and Control Letters, Vol. 60, No. 6, 06.2011, p. 398-405.

Research output: Contribution to journalArticle

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