具有双Allee效应的时滞扩散捕食-食饵模型的时空动力学  

SPATIOTEMPORAL DYNAMICS OF A DELAYED DIFFUSIVE PREDATOR-PREY MODEL WITH DOUBLE ALLEE EFFECT

作　　者：练清清 裴鑫萍 陈云珊 蒙伟明 梁盛 汤小松[1] LIAN Qing-qing;PEI Xin-ping;CHEN Yun-shan;MENG Wei-ming;LIANG Sheng;TANG Xiao-song(School of Mathematics and Physics,Jinggangshan University,Ji’an,Jiangxi 343009,China;School of Electronics and Information Engineering,Jinggangshan University,Ji’an,Jiangxi 343009,China)

机构地区：[1]井冈山大学数理学院,江西吉安343009 [2]井冈山大学电子与信息工程学院,江西吉安343009

出　　处：《井冈山大学学报（自然科学版）》2021年第6期1-7,共7页Journal of Jinggangshan University (Natural Science)

基　　金：国家自然科学基金项目(11761038);江西省教育厅科技计划项目(GJJ180583);江西省大学生创新创业训练计划项目(S202010419044);2019年井冈山大学校级大学生创新创业训练计划项目(2019-74)。

摘　　要：研究了一类具有双Allee效应的时滞扩散捕食-食饵模型。以Allee阈值和时滞为分支参数,利用特征方程和分析技巧讨论了该模型正平衡点的稳定性、扩散诱发的Turing不稳定和时滞诱发的Hopf分支问题。最后,通过数值模拟,获得了该模型的空间周期解和时空斑图,并验证了所得结果的正确性。A delayed diffusive predator-prey model with double Allee effect was investigated in this paper.Allee threshold value and delay was chosen as bifurcation parameter,the stability of the positive equilibrium,Turing instability deduced by diffusion and the existence of Hopf bifurcation deduced by delay for this model were discussed by using the characteristic equation and mathematical analysis skills.At last,by performing numerical simulations,the spatial homogeneous periodic solution of this model was obtained,and the validity of theoretical results was illustrated.

关 键 词：捕食-食饵模型 双Allee效应 周期解 时空斑图 

分 类 号：O175.26[理学—数学]