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 (https://doi.org/10.1016/j.jmaa.2010.10.053)
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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.
ORCID iDs
Li, Xiaoyue, Gray, Alison ORCID: https://orcid.org/0000-0002-6273-0637, Jiang, Daqing and Mao, Xuerong ORCID: https://orcid.org/0000-0002-6768-9864;-
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Item type: Article ID code: 29081 Dates: DateEvent1 April 2011PublishedSubjects: Science > Mathematics > Probabilities. Mathematical statistics Department: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 07 Mar 2011 23:24 Last modified: 23 Dec 2024 01:10 URI: https://strathprints.strath.ac.uk/id/eprint/29081