报告摘要: This paper investigates an initial and boundary value problem for the reaction-diffusion equations, which can be considered as a linearized form of the advective Fisher-KPP equations. It is demonstrated that all solutions exhibit chaotic behavior when the three parameters of the reaction-diffusion equation vary above a specific surface. However, stable solutions are obtained both on and below this surface within a particular subset of initial values. Therefore, a criterion that serves as a necessary and sufficient condition for chaos is deduced. The chaos and stability of the nonhomogeneous initial boundary value problem are further studied. Finally, three numerical examples are provided to illustrate the validity of the obtained results.

报告时间：2025年3月17日（周一）上午9:00-10:30

报告地点：线上，腾讯会议：292-780-317

报告人简介：

杨启贵，理学博士，二级教授，博士生导师，华南理工大学教学名师。主要从事微分方程几何理论、混沌动力系统、随机动力系统及其应用的研究与教学工作，研究系统简单到何种程度仍然具有混沌复杂性，揭示混沌系统混沌机理与复杂动力学特征。 曾获广西科技进步一等奖(排名：1/4)和广东省高等教育省级教学成果二等奖(排名：2/5)，连续3次广东省优秀博士论文指导教师等。至今为止，国内外发表论文150多篇，SCI正面他引2800多次。主持多项国家和省部级项目。已培养出站博士后5人、毕业博士25人（其中2名留学生）、硕士38人，现在读博士生5人和硕士生6人。