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| 摘要: |
| 本文主要研究了一种带有时滞的三物种模型,其中一个物种以另外两个合作的物种为食物.首先,利用比较原理和随机分析理论,建立了平稳分布的准则;其次,利用初值的假设和比较原理,给出了物种的生存性或者灭绝性的充分条件;最后,结合矩阵理论,得到了解的分布平稳,且弱收敛到唯一的一个遍历不变分布. |
| 关键词: 捕食模型 平稳分布 Itô 's公式 |
| DOI： |
| 分类号:O211.63;O29 |
| 基金项目:国家自然科学基金(11901158; 11771123; 12171247); 南京信息工程大学启动基金资助. |
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| STOCHASTIC DYNAMICS ANALYSIS OF COOPERATIVE PREDATOR-PREY MODEL WITH TIME DELAY |
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WANG Xiao-huan,Lü Guang-ying,YANG Ya-nan
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| Abstract: |
| In this paper, a three species model with time delay is studied, in which one species feeds on the other two cooperative species. Firstly, using comparison principle and stochastic analysis theory, the criteria of stationary distribution is established. Secondly, su±cient conditions for the survival or extinction of species are given by using the assumptions on initial data and comparison principle. Finally, combining matrix theory, the stationary distribution of solutions is obtained and weakly converges to a unique ergodic invariant distribution. |
| Key words: predator-prey model stationary distribution Itô 's formula |
