| 摘要: |
| 针对一类Holling II捕食者-食饵模型, 在模型系数与时间相关并具有两个噪声扰动的环境下, 讨论了该模型系统的一些动力学行为问题。为了研究模型长时间的动力学特征, 利用反证法证得了模型正解的存在唯一性, 确保了模型正解的稳定性；再通过构造Lyapunov函数, 并利用It公式和切比雪夫不等式探究了该模型的随机最终有界性, 保证了模型系统是合理的；进一步考虑系统的持续性和永久存在性, 运用离散Hlder不等式和矩不等式等随机微分不等式探究了其一致Hlder连续性和随机持久性，此外, 还利用指数鞅不等式和Borel-Cantelli引理得到了该系统灭绝的充分性条件；最后, 引入数值模拟验证了所得理论结果的正确性。 |
| 关键词: 捕食者-食饵模型 时间相关系数 It公式 随机最终有界 灭绝 |
| DOI： |
| 分类号: |
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| Analysis of a Predator-prey Model with Time-related Coefficients and Two Parameters Perturbation |
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WEI Ning
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School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210023, China
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| Abstract: |
| For a Holling II predator-prey model with time-related coefficients and two parameters perturbation, some dynamical behaviors of the model are discussed. In order to research the long-term dynamic characteristics of the model, the existence and uniqueness of the positive solution is proved by using contradiction to ensure the stability of the positive solution of the model, and then, by constructing Lyapunov function, and using It formula and Chebyshev inequality, stochastic ultimate boundedness of the model is explored, which ensures that the system is reasonable. Thus, the continuity and permanence of the system can be further considered, and by using discrete Hlder inequality and the moment inequality and other stochastic differential inequalities, uniformly Hlder-continuous and stochastic permanence of the system is obtained. Moreover, the sufficient conditions for the system to be extinct are given by using exponential martingale inequality and Borel-Cantelli lemma. At last, some numerical simulations are introduced to verify the correctness of the theoretical results. |
| Key words: predator-prey model time-related coefficients It formula stochastically ultimate boundedness extinction |
