报告人：刘永建教授

报告时间：2025年7月15日上午10:00-11:00

报告地点：数学与信息学院数学系715室

报告摘要：Research on bifurcations at infinity in three-dimensional piecewise-smooth nonlinear vector fields remains scarce in the existing literature. This paper aims to bridge this gap by investigating bifurcations at infinity in general 3D piecewise-smooth quadratic vector fields. We derive the expression for the sliding vector field in the switching region at infinity utilizing the Poincar\'{e} compactification and the Filippov convention. Then, we establish the conditions under which the 36-parameter family exhibits local codimension-0 singularities and codimension-1 bifurcations at infinity. These findings offer valuable insights into the complex dynamics of piecewise smooth nonlinear vector fields. Last but not least, the main results are applied to two models of three-dimensional variable-boostable chaotic flows, whose vector fields contain only square (e.g., $x^{2}$, $y^{2}$ and $z^{2}$) or cross terms (e.g., $xy$, $yz$ and $zx$), and the phase portraits of the dynamic behaviors at infinity are described.

报告人简介：刘永建，二级教授，博士生导师，广西八桂学者，广西优秀教师，广西高校卓越学者，系统科学广西一流学科负责人，广西自然科学基金创新研究团队负责人，曾获广西科学技术奖自然科学奖二等奖、三等奖各1项，广西高校自治区级教学成果奖二等奖1项。主要从事微分方程定性/稳定性理论、混沌与分支理论、微分包含理论的研究。在混沌复杂性分析、吸引子几何解析等方面做出大量工作，近期在具有不连续结构微分系统的定性分析方法研究上获得了一些新结果。主持获得国家自然科学基金项目4项、广西自然科学基金项目4项。

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