Picture water droplets

Developing mathematical theories of the physical world: Open Access research on fluid dynamics from Strathclyde

Strathprints makes available Open Access scholarly outputs by Strathclyde's Department of Mathematics & Statistics, where continuum mechanics and industrial mathematics is a specialism. Such research seeks to understand fluid dynamics, among many other related areas such as liquid crystals and droplet evaporation.

The Department of Mathematics & Statistics also demonstrates expertise in population modelling & epidemiology, stochastic analysis, applied analysis and scientific computing. Access world leading mathematical and statistical Open Access research!

Explore all Strathclyde Open Access research...

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

[img]
Preview
PDF
Logistic_with_Markovian_switching_edited_xm.pdf
Preprint

Download (202kB) | Preview

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.