### Abstract

Language | English |
---|---|

Pages | 427-448 |

Number of pages | 21 |

Journal | Journal of Computational and Applied Mathematics |

Volume | 232 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2009 |

### Fingerprint

### Keywords

- brownian motion
- stochastic differential equation
- generalized It^o's formula
- markov chain
- stochastic permanence.

### Cite this

*Journal of Computational and Applied Mathematics*,

*232*(2), 427-448. https://doi.org/10.1016/j.cam.2009.06.021

}

*Journal of Computational and Applied Mathematics*, vol. 232, no. 2, pp. 427-448. https://doi.org/10.1016/j.cam.2009.06.021

**Population dynamical behavior of Lotka-Volterra system under regime switching.** / Li, Xiaoyue; Jiang, Daqing; Mao, Xuerong; National Natural Science Foundation of China (Funder); Royal Society of Edinburgh (Funder).

Research output: Contribution to journal › Article

TY - JOUR

T1 - Population dynamical behavior of Lotka-Volterra system under regime switching

AU - Li, Xiaoyue

AU - Jiang, Daqing

AU - Mao, Xuerong

AU - National Natural Science Foundation of China (Funder)

AU - Royal Society of Edinburgh (Funder)

PY - 2009

Y1 - 2009

N2 - In this paper, we investigate a Lotka-Volterra system under regime switching dx(t) = diag(x1(t); : : : ; xn(t))[(b(r(t)) + A(r(t))x(t))dt + (r(t))dB(t)]; where B(t) is a standard Brownian motion. The aim here is to find out what happens under regime switching. We first obtain the sufficient conditions for the existence of global positive solutions, stochastic permanence and extinction. We find out that both stochastic permanence and extinction have close relationships with the stationary probability distribution of the Markov chain. The limit of the average in time of the sample path of the solution is then estimated by two constants related to the stationary distribution and the coefficients. Finally, the main results are illustrated by several examples.

AB - In this paper, we investigate a Lotka-Volterra system under regime switching dx(t) = diag(x1(t); : : : ; xn(t))[(b(r(t)) + A(r(t))x(t))dt + (r(t))dB(t)]; where B(t) is a standard Brownian motion. The aim here is to find out what happens under regime switching. We first obtain the sufficient conditions for the existence of global positive solutions, stochastic permanence and extinction. We find out that both stochastic permanence and extinction have close relationships with the stationary probability distribution of the Markov chain. The limit of the average in time of the sample path of the solution is then estimated by two constants related to the stationary distribution and the coefficients. Finally, the main results are illustrated by several examples.

KW - brownian motion

KW - stochastic differential equation

KW - generalized It^o's formula

KW - markov chain

KW - stochastic permanence.

UR - http://www.sciencedirect.com/science/journal/03770427

U2 - 10.1016/j.cam.2009.06.021

DO - 10.1016/j.cam.2009.06.021

M3 - Article

VL - 232

SP - 427

EP - 448

JO - Journal of Computational and Applied Mathematics

T2 - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

IS - 2

ER -