华东师范大学学报（自然科学版） >

2024 , Vol. 2024 >Issue 2: 1 - 13

DOI: https://doi.org/10.3969/j.issn.1000-5641.2024.02.001

数学

一类纯跳种群系统的遍历性

  • 张振中 ,
  • 陈业勤 ,
  • 刘慧媛 ,
  • 李新平 ,
  • 赵馨
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  • 1. 东华大学 理学院, 上海　201620
    2. 上海立信会计金融学院 统计与数学学院, 上海　201209
    3. 湖南理工学院 数学学院, 湖南 岳阳　414006
张振中, 男, 教授, 研究方向为受控的混杂跳扩散系统及应用. E-mail: zzzhang@dhu.edu.cn

收稿日期: 2022-10-30

  网络出版日期: 2024-03-18

基金资助

国家自然科学基金(12171081); 上海市自然科学基金(23ZR1402600); 国家社会科学基金(21BGL188); 湖南省教育厅科研项目(22C0365); 上海市启明星计划扬帆专项(22YF1400900); 东华大学虚拟仿真实验教学项目; 东华大学一流本科课程(DHYLA-2022-23); 东华大学偏微分方程示范教研室(SFJYS2021-05)

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Ergodicity for a class of pure-jump population systems

  • Zhenzhong ZHANG ,
  • Yeqin CHEN ,
  • Huiyuan LIU ,
  • Xinping LI ,
  • Xin ZHAO
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  • 1. College of Science, Donghua University, Shanghai　201620, China
    2. School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai　201209, China
    3. School of Mathematics, Hunan Institute of Science and Technology, Yueyang, Hunan　414006, China

Received date: 2022-10-30

  Online published: 2024-03-18

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摘要

为了刻画随机环境与重大突变因素对种群的影响, 本文考虑一类由马氏链与纯跳稳定过程驱动互惠种群模型. 首先, 讨论了该种群模型具有全局正解性. 其次, 给出了该模型的遍历性的充分条件. 最后, 探究了该模型的正常返的条件.

关键词： α-稳定过程; 马氏链; 遍历性; 正常返

本文引用格式

张振中 , 陈业勤 , 刘慧媛 , 李新平 , 赵馨 . 一类纯跳种群系统的遍历性[J]. 华东师范大学学报（自然科学版）, 2024 , 2024(2) : 1 -13 . DOI: 10.3969/j.issn.1000-5641.2024.02.001

Abstract

To characterize the effects of stochastic environment and major mutation factors on populations, we consider a class facultative population system based on Markov chains and pure-jump stable processes. First of all, the existence and uniqueness of a global positive solution of the proposed model is discussed. Then, sufficient conditions for ergodicity are specified. Finally, conditions for positive recurrence of the model are presented.

Key words： α-stable processes; Markov chains; ergodicity; positive recurrence

参考文献

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