在线咨询
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 ›› 2025, Vol. 42 ›› Issue (3): 425-438.doi: 10.3969/j.issn.1005-3085.2025.03.003doi: 32411.14.1005-3085.2025.03.003

• • 上一篇    下一篇

一类非线性尺度等级结构捕食模型的稳定性

陈伟城,  王战平   

  1. 宁夏大学数学统计学院，银川 750021
  • 收稿日期:2022-09-05 接受日期:2023-02-03 出版日期:2025-06-15 发布日期:2025-06-05
  • 通讯作者: 王战平 E-mail: wang_zp@nxu.edu.cn
  • 基金资助:
    国家自然科学基金 (72464026)；宁夏自然科学基金 (2023AAC03114)；宁夏高等学校一流学科建设项目 (NXYLXK2021A03).

Stability for a Class of Nonlinear Predator-prey Model with Hierarchical Size-structured Populations

CHEN Weicheng,     WANG Zhanping   

  1. School of Mathematics and Statistics, Ningxia University, Yinchuan 750021
  • Received:2022-09-05 Accepted:2023-02-03 Online:2025-06-15 Published:2025-06-05
  • Contact: Z. Wang. E-mail address: wang_zp@nxu.edu.cn
  • Supported by:
    The National Natural Science Foundation of China (72464026); the Natural Science Foundation of Ningxia (2023AAC03114); the First-class Discipline Construction Project in Ningxia Colleges And Universities (NXYLXK2021A03).

摘要：

在自然界中，很多生物种群都存在着与人类社会相似的等级结构，其中种群个体的年龄和尺度都是影响种群等级结构的重要因素，并且个体尺度在生物种群的等级结构中占主导地位的现象更加明显和普遍。因此，在基于种群中尺度较大的个体在获取食物和繁衍后代等方面具有较大优势的背景下，研究了一类非线性尺度等级结构捕食模型正平衡态的存在性和零平衡态的稳定性问题。利用非零元不动点定理，证明了该模型至少存在一个正平衡态，推导零平衡态的特征方程，建立Lyapunov函数得到零平衡态的局部和全局渐近稳定性判据。最后，对零平衡态进行数值模拟，验证零平衡态的稳定性结论。

关键词: 尺度结构, 捕食模型, 正平衡态, 稳定性, 数值模拟

Abstract:

In natural world, many biological populations exist in a hierarchical structure which is similar to human societies, both the age and size of individual populations are important factors to influence the hierarchical structure of populations, and the dominance of the individual size in the hierarchical structure of biological populations has more pronounced and widespread. Therefore, based on the fact that individuals with larger size in a population have a greater advantage in obtaining food and reproducing offspring, this paper researches the existence of positive equilibria state and the stability of zero equilibria state of a nonlinear predator-prey model with hierarchical size-structured. A non-zero fixed point theorem is used to show that there is at least one positive equilibrium state in the model. The stability criterion of the zero equilibrium state is obtained by deriving the characteristic equation of the zero equilibrium state and constructing the Lyapunov function. Finally, present some numerical experiments of zero equilibrium state to verify the conclusions.

Key words: size-structured, predator-prey model, positive equilibria, stability, numerical experiments