Bifurcation near a transcritical singularity in planar singularly perturbed systems

：沈建和（福建师范大学）
：2023-02-16 14:40
：厦大海韵园实验楼105报告厅

报告人：沈建和（福建师范大学）

时  间：2023年2月16日下午14:40-15:20

地  点：厦大海韵园实验楼105报告厅

内容摘要:

Based on the geometric singular perturbation theory and the blow-up technique, we classify all bifurcation phenomena of the flow near a transcritical singularity in a planar singularly perturbed system which has no a breaking parameter. As a byproduct, it is shown that the bifurcation delay cannot occur near the singularity of the system. In this situation, the flow either approaches to this singularity, or escapes from it along the critical fiber depending on the choice of the parameters of the system. Numerical simulations are provided to a modified Leslie-Gower model for verifying our theoretical results.

 

个人简介：

沈建和，福建师范大学数学与统计学院教授、博士生导师；兼任中国数学会奇异摄动专业委员会副主任、美国《数学评论》和德国《数学文摘》评论员等；研究方向为奇异摄动理论及应用；已在《Philosophical Transactions of the Royal Society A》《Physica D: Nonlinear Phenomenon》《Journal of Dynamics and Differential Equations》《Discrete and Continuous Dynamical Systems》等杂志发表论文约20篇；主持或主持完成国家自然科学基金面上项目和青年项目、中国博士后科学基金、福建省自然科学基金重点项目和面上项目等多项；入选百千万人才工程省级人选（2019年）和福建省雏鹰计划青年拔尖人才计划（2020年）等。