# American Institute of Mathematical Sciences

July  2015, 20(5): 1481-1497. doi: 10.3934/dcdsb.2015.20.1481

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

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

Received  November 2013 Revised  December 2014 Published  May 2015

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.
Citation: Yangzi Hu, Fuke Wu. The improved results on the stochastic Kolmogorov system with time-varying delay. Discrete & Continuous Dynamical Systems - B, 2015, 20 (5) : 1481-1497. doi: 10.3934/dcdsb.2015.20.1481
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