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Stochastic population dynamics under regime switching II

Mao, X. and Luo, Q. and , National Natural Science Foundation of China (Funder) and , EPSRC (UK) (Funder) and , London Mathematical Society (Funder) and , Edinburgh Mathematical Society (Funder) (2009) Stochastic population dynamics under regime switching II. Journal of Mathematical Analysis and Applications, 355 (2). pp. 577-593. ISSN 0022-247X

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Abstract

This is a continuation of our paper [Q. Luo, X. Mao, Stochastic population dynamics under regime switching, J. Math. Anal. Appl. 334 (2007) 69-84] on stochastic population dynamics under regime switching. In this paper we still take both white and color environmental noise into account. We show that a sufficient large white noise may make the underlying population extinct while for a relatively small noise we give both asymptotically upper and lower bound for the underlying population. In some special but important situations we precisely describe the limit of the average in time of the population.