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EPRC is a leading institute in Europe for comparative research on public policy, with a particular focus on regional development policies. Spanning 30 European countries, EPRC research programmes have a strong emphasis on applied research and knowledge exchange, including the provision of policy advice to EU institutions and national and sub-national government authorities throughout Europe.

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Population dynamical behavior of Lotka-Volterra system under regime switching

Li, Xiaoyue and Jiang, Daqing and Mao, Xuerong, National Natural Science Foundation of China (Funder), Royal Society of Edinburgh (Funder) (2009) Population dynamical behavior of Lotka-Volterra system under regime switching. Journal of Computational and Applied Mathematics, 232 (2). pp. 427-448. ISSN 0377-0427

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Abstract

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.