基于自由扩散下被捕食者-捕食者模型的图灵不稳定分析  

Turing Instability analysis based on predator prey model with free diffusion

作　　者：赖婷 袁权 杨喜艳 王浩华 Lai Ting;Yuan Quan;Yang Xiyan;Wang Haohua(School of Sciences,Hainan University,Haikou 570228,China;Hainan Key Laboratory for Engineering Modeling and Statistical Calculation,Guangzhou 510521,China;School of Finanical Mathematics and Statisitcs,Guangdong University of Finance,Haikou 570228,China;Ministry of Education Key Laboratory for Genetics&Germplasm Enhancement of Tropical Specialty Forest and Flowers and Plants,Haikou 570228,China)

机构地区：[1]海南大学理学院,海南海口570228 [2]海南省工程建模与统计计算重点实验室,广东广州510521 [3]广东金融学院金融数学与统计学院,海南海口570228 [4]海南大学热带特色林木花卉遗传与种质创新教育部重点实验室,海南海口570228

出　　处：《海南大学学报（自然科学版）》2023年第2期133-144,共12页Natural Science Journal of Hainan University

基　　金：国家自然科学基金(12261028,11761025,11961018);海南省高层次人才项目(120RC451,2019RC168);海南省重点研发项目(ZDYF2021SHFZ231);广东省普通高等重点领域专项(2022ZDZX2045)。

摘　　要：研究了具有Beddington-DeAngelis功能反应的被捕食者-捕食者模型在自由扩散模式下的图灵不稳定性.分析了系统在无自由扩散情形下的耗散性和一致持久性的充分条件以及非负平衡点的局部稳定性,并通过刻画系统非负平衡点的图灵不稳定性条件,确定产生图灵斑图的分岔参数满足的条件以及相应的图灵区域.数值实验结果验证了系统的稳定性,揭示了波色数、分岔参数和交叉扩散系数对斑图产生的定量影响.In the report,the Turing instability of the predator-prey model with Beddington-DeAngelis functional response in free diffusion were studied.The sufficient conditions of dissipation and uniform persistence of the system without free diffusion and the local stability of non-negative equilibrium point were analyzed.The condition of Turing instability of the non-negative equilibrium point of the system were characterized,and the condition for producing the bifurcation parameters of Turing pattern and the corresponding Turing region were determined.The numerical results indicated that the system is stable and the wave chromatic number,bifurcation parameters and cross diffusion coefficient are important factors for the generation of Turing pattern.

关 键 词：Beddington-DeAngelis功能反应 被捕食者-捕食者模型 图灵不稳定性 图灵斑图 

分 类 号：R181[医药卫生—流行病学] O232[医药卫生—公共卫生与预防医学]