Journal
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
Volume 354, Issue 14, Pages 6119-6137Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jfranklin.2017.07.012
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Funding
- National Natural Science Foundation of China [11401136, 11501148]
- Shandong Provincial Natural Science Foundation, China [ZR2014AQ010, ZR2015AQ002]
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The existence and uniqueness of stationary distribution and ergodic properties of a stochastic system are obtained. Especially, different from the existing methods, a new method is introduced to analyze almost sure permanence and uniform boundedness of the stochastic predator-prey model. This new idea is based on geometric structure of invariant set for a stochastic system. More specifically, we obtain our main conclusions by showing the invariant set for the stochastic population system lies in the interior of the first quadrant. It is interesting and surprising that the stochastic population model can guarantee a uniform boundedness almost surely. Some numerical simulations are carried out to support our results. (C) 2017 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
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