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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2020, Vol. 37 ›› Issue (1): 27-42.doi: 10.3969/j.issn.1005-3085.2020.01.003

• • 上一篇    下一篇

污染环境中广义单种群模型的动力学行为分析

曹  明,  王  霞,  唐三一   

  1. 陕西师范大学数学与信息科学学院，西安 710119
  • 收稿日期:2017-08-15 接受日期:2018-11-01 出版日期:2020-02-15 发布日期:2020-04-15
  • 通讯作者: 唐三一 E-mail: sytang@snnu.edu.cn
  • 基金资助:
    国家自然科学基金(11601301; 11471201)；中央高校基本科研业务费专项资金(GK201803006).

Dynamical Behavior Analysis of a Generalized Single-species Population Model in a Polluted Environment

CAO Ming,  WANG Xia,  TANG San-yi   

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710119
  • Received:2017-08-15 Accepted:2018-11-01 Online:2020-02-15 Published:2020-04-15
  • Contact: S. Tang. E-mail address: sytang@snnu.edu.cn
  • Supported by:
    The National Natural Science Foundation of China (11601301; 11471201); the Fundamental Research Funds for the Central Universities (GK201803006).

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摘要： 人类社会现代工农业的飞速发展和其他生产活动所造成的环境污染问题，已经成为最重要的生态学问题之一， 生态环境的严重污染已经威胁到了物种的生存．为了研究污染环境中种群的生存问题，本文中，我们建立了一个新的污染环境中的广义单种群模型来研究污染环境中环境毒素和食物链毒素对种群生存的影响．利用平均积分法研究得到了种群一致持久、平均非持久、平均弱持久和灭绝的充分条件，以及种群平均弱持久与灭绝之间的阈值条件．该结果对于保护物种生存和治理环境提供了可靠的科学依据．

关键词: 广义 Logistic 模型, 污染环境, 种群, 持久, 灭绝

Abstract: The environmental pollution problem caused by the rapid development of modern industry and agriculture and other production activities has become one of the most important ecological problems. In this paper, a new generalized single-species population model in polluted environment is established to study the influence of environmental toxins and food chain toxins on the existence of the specie. By using the average integral method, sufficient conditions for uniform persistence, non-persistent in the mean, weak persistence in the mean and extinction, and the threshold between weak persistence and extinction of the population are obtained. These results provide reliable scientific basis for the conservation of species and the management of the environment.

Key words: generalized Logistic model, polluted environment, population, persistence, extinction

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