The improved results on the  stochastic Kolmogorov system with time-varying delay

Yangzi Hu; Fuke Wu

doi:10.3934/dcdsb.2015.20.1481

Article Contents

2015, Volume 20, Issue 5: 1481-1497. Doi: 10.3934/dcdsb.2015.20.1481

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The improved results on the stochastic Kolmogorov system with time-varying delay

Yangzi Hu^1, and
Fuke Wu^2,

1.
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074
2.
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074

Received: October 31, 2013

Revised: November 30, 2014

Published: June 2015

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Abstract

This paper discusses the stochastic Kolmogorov system with time-varying delay. Under two classes of sufficient conditions, this paper solves the non-explosion, the moment boundedness and the polynomial pathwise growth simultaneously. This is an important improvement for the existing results, since the moment boundedness and the polynomial pathwise growth do not imply each in general. Moreover, these two classes of conditions only depends on the parameters of the system and are easier to be used. Finally, a two-dimensional Komogorov model is examined to illustrate the efficiency of our result.

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Mathematics Subject Classification: Primary: 60H10, 34A34, 34D40, 34K50.

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