一类具非线性交错扩散和恐惧效应的捕食-食饵模型的Turing分支和空间模式  

Turing bifurcation and spatial pattern of a predator-prey model with nonlinear cross-diffusion and fear effect

作　　者：胡慧 甘文珍(指导) 金龚逸 张凌翔 HU Hui;GAN Wenzhen;JIN Gongyi;ZHANG Lingxiang(School of Mathematics and Physics,Jiangsu University of Technology,Changzhou 213001,China;College of Finance and Statistics,Hunan University,Changsha 410082,China)

机构地区：[1]江苏理工学院数理学院,江苏常州213001 [2]湖南大学金融与统计学院,湖南长沙410082

出　　处：《江苏理工学院学报》2023年第4期66-74,共9页Journal of Jiangsu University of Technology

基　　金：江苏省大学生创新创业训练计划项目“具扩散的传染病模型的动力学行为和空间模式研究”(202211463044Z)。

摘　　要：研究了一类具非线性交错扩散和恐惧效应的捕食-食饵模型的Turing分支和空间模式。首先,利用线性化方法和特征值理论,研究了仅具有自扩散的系统中一个正平衡点的稳定性;其次,讨论了具有交错扩散的系统中该正平衡点的稳定性;最后,利用数值模拟呈现具有交错扩散的偏微系统的空间模式。研究结果表明:在一定条件下,自扩散不影响正平衡点的局部渐近稳定性,但非线性交错扩散会使正平衡点不稳定,从而产生Turing分支。This paper mainly studies the Turing bifurcation and spatial pattern of a predator-prey model with nonlinear cross-diffusion and fear effect.First,the stability of a positive equilibrium point in the system with only self-diffusion is studied by using the linearization method and eigenvalue theory.Second,the stability of the posi-tive equilibrium point in the system with cross-diffusion is discussed.Finally,the spatial pattern of the system with cross-diffusion is presented by numerical simulations.The results show that under certain conditions,self-diffusion does not affect the local asymptotic stability of the positive equilibrium point,but the nonlinear cross diffusion can make the positive equilibrium point unstable,resulting in Turing bifurcation.

关 键 词：恐惧效应 捕食与被捕食模型 非线性交错扩散 Turing分支 空间模式 

分 类 号：O175.26[理学—数学]