一个扩散模型中恐惧效应与集群行为协同诱导的时空动力学研究  

Spatiotemporal Dynamics Induced by the Interaction Between Fear and Schooling Behavior in a Diffusive Model

作　　者：肖江龙 宋永利 夏永辉 Xiao Jianglong;Song Yongli;Xia Yonghui(School of Mathematical Sciences,Zhejiang Normal University,Zhejiang Jinhua 321004;School of Mathematics,Hangzhou Normal University,Hangzhou 311121;School of Mathematics,Foshan University,Guangdong Foshan 528000)

机构地区：[1]浙江师范大学数学科学学院,浙江金华321004 [2]杭州师范大学数学学院,杭州311121 [3]佛山大学数学学院,广东佛山528000

出　　处：《数学物理学报（A辑）》2024年第6期1577-1594,共18页Acta Mathematica Scientia

基　　金：国家自然科学基金(11931016);浙江省自然科学基金(LZ23A010001,LZ24A010006)

摘　　要：该文研究了在齐次Neumann边界条件下扩散的捕食者--猎物模型的时空动力学.该文研究表明,恐惧和集群行为之间的相互作用产生了非常丰富和有趣的时空动力学.详细讨论了Turing不稳定性和Turing-Hopf分支产生的条件.利用规范型理论对Turing-Hopf分支点附近的时空动力学进行了分类,并用丰富的数值模拟验证了理论分析.最后,总结了恐惧效应对集群行为的巨大影响.发现猎物的集群行为不能抵消高水平的恐惧,但可以抵消低水平的恐惧.此外,恐惧效应与集群行为共同诱发了系统的Turing不稳定性.然而,对于没有集群行为的系统,恐惧效应既不会改变共存平衡点的稳定性,也不会引起系统产生周期解或Turing不稳定性.In this paper,we study the spatiotemporal dynamics in a diffusive predator-prey model with the homogeneous Neumann boundary condition.Our study indicates that the interaction between fear and schooling behavior induces very rich and interesting spatiotemporal dynamics.The conditions for Turing instability and Turing-Hopf bifurcation emerging are explored at length.By utilizing the normal form method,the spatiotemporal dynamics of the spatial model near the Turing-Hopf bifurcation point are classified.And rich numerical simulations are used to confirm the theoretical analysis.Finally,we summarize the great influence of the fear effect and schooling behavior.We found that the schooling behavior of prey cannot counteract high-level fear,while it offsets the low-level fear.Moreover,the fear effect induces Turing instability of the system with the schooling behavior.However,the fear effect neither changes the stability of coexistence equilibrium,nor induces periodic solutions or Turing instability of the system without the schooling behavior.

关 键 词：Turing-Hopf分支 Turing不稳定性 集群行为 恐惧效应 动力学分类 捕食者-猎物模型 

分 类 号：O175.23[理学—数学]