应兰州大学数学与统计学院李万同教授和孙建文教授邀请，首都师范大学数学科学学院邹兰教授将于2025年1月9日（星期四）进行在线学术报告，欢迎广大师生参加。

题 目：Bifurcations of codimension 4 in a Leslie-type predator-prey model with Allee effects

时 间：1月9日（星期四）10：00

腾讯会议：626-657-014

摘要：We explore a Leslie-type predator-prey model with simplified Holling IV functional response and Allee effects in prey. It is shown that the model can undergo a sequence of bifurcations including cusp, focus and saddle-node types nilpotent bifurcations of codimension four and a degenerate Hopf bifurcation of codimension up to four as the parameters vary. Our results indicate that Allee effects can induce richer dynamics and bifurcations, especially high sensitivities on both parameters and initial densities for coexistence and oscillations of both populations. Moreover, strong Allee effects (M > 0) (or `transitional Allee effects' (M = 0) with large predation rates) can cause the coextinction of both populations with some positive initial densities, while weak Allee effects (M < 0) (or transitional Allee effects with small predation rates) make both populations with positive initial densities persist forever. Finally, numerical simulations present some illustrations scarce in two-population models, such as the coexistence of three limit cycles and three positive equilibria.

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报告人简介

邹兰，首都师范大学数学科学学院教授。2010年6月在四川大学获理学博士学位，多次访问美国迈阿密大学数学系。目前研究方向为微分方程与动力系统、生物数学，特别关注传染病传播动力学、病毒动力学、生态种群动力学等建模及其定性理论、分岔理论等。任中国数学会生物数学专委会委员，CSIAM数学生命科学专委会委员。研究结果发表在SIAM Appl Math, PLoS Neglect Trop Dis, Bull. Math. Biol.， J Theor Biol，J. Nonlinear Sci.，J. Differential Equations 等国际期刊。先后主持国家自然科学基金青年基金、面上基金，参与国家自然科学基金重点基金一项。

甘肃应用数学中心

数学与统计学院

萃英学院

2025年1月7日