摘要
考虑了Holling-Ⅱ型功能反应项和改进的Leslie-Gower项,建立了具有双Allee效应的交叉扩散捕食-猎物模型,分析了无扩散系统下正平衡点的存在性和稳定性,给出了有扩散项作用下发生Turing不稳定的条件.同时重点研究了双Allee效应对斑图形成、结构改变和演化速度的影响机制.研究发现:在扩散驱动系统稳定的情况下,Allee效应能够诱导斑图的形成;在扩散驱动系统不稳定的情况下,Allee效应能够实现斑图结构的改变.此外,在不同的Allee效应系数下,系统到达稳定纯色斑图和稳定混色斑图的时间各不同,即Allee效应能够改变斑图的演化速度.因此,双Allee效应在捕食-猎物系统中对Turing斑图的形成和演化具有至关重要的作用。
The Holling-Ⅱ functional responses and an improved Leslie-Gower term were considered to establish a cross-diffusion predator-prey model with double Allee effects.The existence and stability of positive equilibrium points were analyzed in the absence of diffusion to provide conditions for Turing instability under the diffusion effects.The influential mechanisms of the double Allee effects on the pattern formation,the structural changes,and the evolutionary speed was mainly investigated.The findings reveal that,in stable diffusion-driven systems,the Allee effects can induce pattern formation;conversely,in unstable systems,the Allee effects can lead to structural changes in patterns.Additionally,the time required for the system to reach stable homogeneous and mixed patterns varies with different Allee effects coefficients,indicating that the Allee effects can significantly alter the evolutionary speed of patterns.Therefore,the double Allee effects plays a crucial role in the formation and evolution of Turing patterns in predator-prey systems.
作者
阳锋
肖敏
杨正午
段代凤
杨鑫松
曹进德
YANG Feng;XIAO Min;YANG Zhengwu;DUAN Daifeng;YANG Xinsong;CAO Jinde(College of Automation and College of Artificial Intelligence,Nanjing University of Posts and Telecommunications,Nanjing 210023,P.R.China;College of Electronics and Information Engineering,Sichuan University,Chengdu 610065,P.R.China;School of Mathematics,Southeast University,Nanjing 211189,P.R.China)
出处
《应用数学和力学》
北大核心
2026年第1期90-100,共11页
Applied Mathematics and Mechanics
基金
国家自然科学基金(62073172)
江苏省自然科学基金(BK20221329)。
