具有集群行为的捕食者-食饵反应扩散模型的动力学分析  

Analysis for Dynamics of Predator-prey Reaction-diffusion Model with Schooling Behavior

作　　者：郑薇 张存华[1] ZHENG Wei;ZHANG Cunhua(Department of Mathematics,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学数学系,甘肃兰州730070

出　　处：《洛阳理工学院学报（自然科学版）》2024年第3期70-77,共8页Journal of Luoyang Institute of Science and Technology：Natural Science Edition

基　　金：国家自然科学基金项目(12261054).

摘　　要：考虑一类具有集群行为和齐次Neumann边界条件的捕食者-食饵反应扩散系统。通过分析系统在正常数平衡解处线性化系统的特征值问题,获得了正常数平衡解的局部渐近稳定性、Turing不稳定性、Hopf分岔和Turing-Hopf分岔的存在性。同时,通过数值模拟对所获得的理论结果进行了适当的数值验证。A class of predator-prey reaction-diffusion model with schooling behavior and homogeneous Neumann boundary conditions is considered.The local asymptotic stability,Turing instability,the existence of Hopf bifurcation and Turing-Hopf bifurcation of the constant positive equilibrium solution are obtained by analyzing the associated eigenvalue problem.Also,the theoretical results are verified by numerical simulation.

关 键 词：集群行为 稳定性 Turing不稳定性 HOPF分岔 Turing-Hopf分岔 

分 类 号：O175.26[理学—数学]