Li, X. and Jiang, D. and Mao, X. and , National Natural Science Foundation of China (Funder) and , Royal Society of Edinburgh (Funder) (2009) Population dynamical behavior of LotkaVolterra system under regime switching. Journal of Computational and Applied Mathematics, 232 (2). pp. 427448. ISSN 03770427

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Abstract
In this paper, we investigate a LotkaVolterra 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 nd out what happens under regime switching. We rst obtain the sucient conditions for the existence of global positive solutions, stochastic permanence, extinction. We nd out that both stochastic permanence and extinction have close relationships with the stationary probability distribution of the Morkov 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 coecients. Finally, the main results are illustrated by several examples.
Item type:  Article 

ID code:  14033 
Keywords:  brownian motion, stochastic differential equation, generalized It^o's formula, markov chain, stochastic permanence., Mathematics, Computational Mathematics, Applied Mathematics 
Subjects:  Science > Mathematics 
Department:  Faculty of Science > Mathematics and Statistics 
Depositing user:  Mrs Carolynne Westwood 
Date Deposited:  11 Jan 2010 16:39 
Last modified:  21 May 2015 11:09 
URI:  http://strathprints.strath.ac.uk/id/eprint/14033 
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