由截尾α-稳定过程驱动的种群系统的遍历性

doi:10.3969/j.issn.1000-5641.2025.06.001

华东师范大学学报（自然科学版） ›› 2025, Vol. 2025 ›› Issue (6): 1-13.doi: 10.3969/j.issn.1000-5641.2025.06.001

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由截尾α-稳定过程驱动的种群系统的遍历性

张振中¹(), 顾笑凡¹, 童俊波², 赵馨¹, 李新平³

1. 东华大学数学与统计学院, 上海　201620
2. 娄底市第一中学, 湖南娄底　417000
3. 湖南理工学院数学学院, 湖南岳阳　414006

收稿日期:2024-03-11 出版日期:2025-11-25 发布日期:2025-11-29
作者简介: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
基金资助:
上海市自然科学基金(23ZR1402600); 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

The ergodicity of population dynamics driven by truncated α-stable processes

Zhenzhong ZHANG¹(), Xiaofan GU¹, Junbo TONG², Xin ZHAO¹, Xinping LI³

1. School of Mathematics and Statistics, Donghua University, Shanghai　201620, China
2. Number One Middle School of Loudi, Loudi, Hunan　417000, China
3. School of Mathematics, Hunan Institute of Science and Technology, Yueyang, Hunan　414006, China

Received:2024-03-11 Online:2025-11-25 Published:2025-11-29

摘要/Abstract

摘要：

为了研究生物种群在复杂环境中的动态行为, 考虑了一个由截尾α-稳定过程驱动的$n$维种群模型. 首先, 建立了一个纯跳情形下的Khasminskii 判别定理; 其次, 讨论了该系统的正则点; 最后, 给出了此类纯跳系统遍历性的一个判别准则.

关键词: 平稳分布, 正则点, 截尾α-稳定过程

Abstract:

In order to study the dynamic behavior of biological populations in complex environments, we consider an n-dimensional population model driven by a truncated α-stable process. First of all, a generalized Khasminskii theorem for pure jump systems has been established. Then, the regular points such a system are discussed. Finally, we give a sufficient criterion to verify ergodicity for such a pure jump population dynamic system.

Key words: stationary distribution, regular point, truncated α-stable processes

中图分类号:

O211.63

张振中, 顾笑凡, 童俊波, 赵馨, 李新平. 由截尾α-稳定过程驱动的种群系统的遍历性[J]. 华东师范大学学报（自然科学版）, 2025, 2025(6): 1-13.

Zhenzhong ZHANG, Xiaofan GU, Junbo TONG, Xin ZHAO, Xinping LI. The ergodicity of population dynamics driven by truncated α-stable processes[J]. J* E* C* N* U* N* S*, 2025, 2025(6): 1-13.

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由截尾α-稳定过程驱动的种群系统的遍历性

The ergodicity of population dynamics driven by truncated α-stable processes

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