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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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Sufficient and necessary conditions of stochastic permanence and extinction for stochastic logistic populations under regime switching

Li, Xiaoyue and Gray, Alison and Jiang, Daqing and Mao, Xuerong (2011) Sufficient and necessary conditions of stochastic permanence and extinction for stochastic logistic populations under regime switching. Journal of Mathematical Analysis and Applications, 376 (1). pp. 11-28. ISSN 0022-247X

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Abstract

In this paper, we prove that a stochastic logistic population under regime switching controlled by a Markov chain is either stochastically permanent or extinctive, and we obtain the sufficient and necessary conditions for stochastic permanence and extinction under some assumptions. In the case of stochastic permanence we estimate the limit of the average in time of the sample path of the solution by two constants related to the stationary probability distribution of the Markov chain and the parameters of the subsystems of the population model. Finally, we illustrate our conclusions through two examples.