具有多种相互作用的 Leslie-Gower 捕食者-猎物系统的时空动力学分析

数学物理学报 ›› 2026, Vol. 46 ›› Issue (1): 143-156.

具有多种相互作用的 Leslie-Gower 捕食者-猎物系统的时空动力学分析

杨正午¹(), 肖敏¹^,^*(), 周颖¹(), 丁洁¹, 赵静¹

¹南京邮电大学自动化学院, 人工智能学院南京 210023
²波兰科学院系统研究所波兰华沙 01-447

收稿日期:2025-01-07 修回日期:2025-06-27 出版日期:2026-02-26 发布日期:2026-01-19
通讯作者: 肖敏 E-mail:njuptyzw2001@163.com;candymanxm2003@aliyun.com;zhouying@njupt.edu.cn
作者简介:杨正午, Email: njuptyzw2001@163.com;
周颖, Email: zhouying@njupt.edu.cn
基金资助:
国家自然科学基金(62073172);江苏省自然科学基金(BK20221329)

Spatiotemporal Dynamics Analysis of a Leslie-Gower Predator-Prey System with Multiple Interactions

Zhengwu Yang¹(), Min Xiao¹^,^*(), Ying Zhou¹(), Jie Ding¹, Jing Zhao¹, Rutkowski Leszek²

¹School of College of Automation and College of Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing 210023
²Systems Research Institute, Polish Academy of Sciences, Poland Warsaw 01-447

Received:2025-01-07 Revised:2025-06-27 Online:2026-02-26 Published:2026-01-19
Contact: Min Xiao E-mail:njuptyzw2001@163.com;candymanxm2003@aliyun.com;zhouying@njupt.edu.cn
Supported by:
NSFC(62073172);Natural Science Foundation of Jiangsu Province(BK20221329)

摘要/Abstract

摘要：

目前关于捕食者-猎物系统的研究大多仅考虑单一相互作用, 难以刻画种群间真实的复杂交互. 因此, 该文基于 Beddington-DeAngelis 功能响应函数和改进的 Leslie-Gower 项, 建立了一个具有恐惧效应、饱和效应、种内竞争、捕食干扰多种相互作用机制的交叉扩散捕食者-猎物系统. 在无扩散系统中, 分析了正平衡点稳定性及猎物种内竞争诱导的 Hopf 分岔条件. 在扩散系统中, 给出了发生 Turing 不稳定的条件, 重点研究了各种相互作用对图灵斑图模式的形成和演化的影响机制. 研究发现, 改变恐惧效应等相互作用的强度以及交叉扩散系数, 会引起图灵斑图模式的转变. 不同的相互作用机制还会在不同程度上改变系统稳定性和图灵斑图模式的稳定速度. 其结果表明, 捕食者与猎物间的相互作用和交叉扩散对系统的动力学行为具有重要影响.

关键词: 相互作用, 交叉扩散, Beddington-DeAngelis 功能响应函数, 改进的 Leslie-Gower, 图灵斑图

Abstract:

Current studies on predator-prey systems mainly consider single interaction mechanisms, which cannot fully characterize the complex ecological interactions between populations. Therefore, this paper establishes a cross-diffusion predator-prey system incorporating multiple interaction mechanisms including fear effects, saturation effects, intraspecific competition, and predator interference, based on the Beddington-DeAngelis functional response function and modified Leslie-Gower terms. For the non-diffusion system, we analyze the stability of positive equilibrium points and the Hopf bifurcation conditions induced by prey intraspecific competition. For the diffusion system, we derive the conditions for Turing instability and focus on investigating how various interaction mechanisms affect the formation and evolution of Turing patterns. The results demonstrate that changing the intensity of interaction mechanisms (such as fear effects) and cross-diffusion coefficients can lead to transitions between different Turing patterns, while different interaction mechanisms can also alter the system stability and the stabilization rate of Turing patterns to varying degrees. The results indicate that interactions between predators and prey, along with cross-diffusion, significantly impact the dynamical behavior of the system.

Key words: interaction, cross-diffusion, Beddington-DeAngelis functional response, modified Leslie-Gower, Turing patterns

中图分类号:

O175.23

杨正午, 肖敏, 周颖, 丁洁, 赵静. 具有多种相互作用的 Leslie-Gower 捕食者-猎物系统的时空动力学分析[J]. 数学物理学报, 2026, 46(1): 143-156.

Zhengwu Yang, Min Xiao, Ying Zhou, Jie Ding, Jing Zhao, Rutkowski Leszek. Spatiotemporal Dynamics Analysis of a Leslie-Gower Predator-Prey System with Multiple Interactions[J]. Acta mathematica scientia,Series A, 2026, 46(1): 143-156.

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