污染环境下具有脉冲输入的随机捕食-食饵模型的动力学研究

数学物理学报 ›› 2019, Vol. 39 ›› Issue (3): 674-688.

污染环境下具有脉冲输入的随机捕食-食饵模型的动力学研究

付盈洁,蓝桂杰,张树文,魏春金*()

集美大学理学院福建厦门 361021

收稿日期:2018-03-13 出版日期:2019-06-26 发布日期:2019-06-27
通讯作者: 魏春金 E-mail:chunjinwei92@163.com
基金资助:
福建省自然科学基金(2016J01667);福建省自然科学基金(2016J05012);福建省自然科学基金(2018J01418)

Dynamics of a Stochastic Predator-Prey Model with Pulse Input in a Polluted Environment

Yingjie Fu,Guijie Lan,Shuwen Zhang,Chunjin Wei*()

School of Sciences, Jimei University, Fujian Xiamen 361021

Received:2018-03-13 Online:2019-06-26 Published:2019-06-27
Contact: Chunjin Wei E-mail:chunjinwei92@163.com
Supported by:
the Fujian Provincial Natural Science Foundation(2016J01667);the Fujian Provincial Natural Science Foundation(2016J05012);the Fujian Provincial Natural Science Foundation(2018J01418)

摘要/Abstract

摘要：

该文研究了污染环境下具有脉冲输入的随机捕食-食饵模型，证明了系统的全局正解的存在唯一性，均值有界性，给出了系统边界周期解以概率1全局吸引的存在条件，并得到了种群灭绝与持续生存的阈值.最后用数值模拟进一步验证了理论结果的正确性.

关键词: 捕食-食饵模型, 毒素脉冲, 随机扰动, 均值有界, 全局吸引

Abstract:

In this paper, we show a stochastic predator-prey model with pulse input in a polluted environment, the existence and uniqueness of the positive global solution and the boundedness of expectation of the system are all proved, the sufficient conditions for the existence and boundedness of periodical solution are obtained, and it is globally attractive with probability 1, and the threshold of population extinction and persistence in the mean are obtained too. Finally, some numerical simulations are carried out to illustrate the main results.

Key words: Predator-prey system, Pulse toxicant, Random disturbance, Mean boundedness, Globally attractivity

中图分类号:

O175.13

付盈洁,蓝桂杰,张树文,魏春金. 污染环境下具有脉冲输入的随机捕食-食饵模型的动力学研究[J]. 数学物理学报, 2019, 39(3): 674-688.

Yingjie Fu,Guijie Lan,Shuwen Zhang,Chunjin Wei. Dynamics of a Stochastic Predator-Prey Model with Pulse Input in a Polluted Environment[J]. Acta mathematica scientia,Series A, 2019, 39(3): 674-688.

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