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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 ›› 2018, Vol. 35 ›› Issue (1): 110-122.doi: 10.3969/j.issn.1005-3085.2018.01.011

• • 上一篇    

随机环境中伴有移民且配对依赖人口数的两性分枝过程（英）

宋明珠,   向亚云   

  1. 铜陵学院数学与计算机学院，铜陵  241000
  • 收稿日期:2014-11-18 接受日期:2017-10-13 出版日期:2018-02-15 发布日期:2018-04-15
  • 基金资助:
    安徽省高校重点科研项目(KJ2016A705)；安徽省高校优秀青年人才支持计划重点项目(gxyqZD2016317)；铜陵大学科研项目(2014tlxy26)；大学生创新创业训练计划(201510383030).

Limiting Behavior of the Bisexual Galton-Watson  Branching Process with Immigration and Population-size-dependent Mating in Random Environments

SONG Ming-zhu,   XIANG Ya-yun   

  1. Department of Mathematics and Computer Science, Tongling University, Tongling 244000
  • Received:2014-11-18 Accepted:2017-10-13 Online:2018-02-15 Published:2018-04-15
  • Supported by:
    The Key University Science Research Project of Anhui Province (KJ2016A705); the Key Projects of Anhui Province University Outstanding Youth Talent Support Program (gxyqZD2016317); the Science Research Project of Tongling University (2014tlxy26); the College Student Innovation and Entrepreneurship Training Program (201510383030).

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摘要： 本文首先介绍了两性分枝过程的发展情况，在前人研究的基础上，本文建立了更符合自然界两性生物繁衍规律的模型，配对依赖当前人口数且伴有移民的两性分枝过程．利用上可加函数的性质，得到了平均增长率的极限．在一定的条件，推导出此过程以概率 1 灭绝的一个充要条件，进而推广了前人的研究成果．

关键词: 分枝过程, 两性分枝过程, 移民, 配对依人口数, 增长率, 灭绝概率

Abstract: Firstly, this paper introduces the development of bisexual Galton-Watson branching process. On the basis of past achievements, a model with population size dependent mating and immigration (BIPSDM) is established in random environments, that is more conform to the fact about bisexual biological reproduction. Then, applying some classical results on superadditive functions, the limit of mean growth rate per mating unit is obtained. Through discussing extinct probability of BIPSDM, a necessary and sufficient condition for BIPSDM to become extinct with probability one was found under certain conditions. Some properties known are enlarged in this article.

Key words: Galton-Watson branching process, bisexual Galton-Watson branching process, immigration, population size dependent mating, growth rate, extinction probability

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