簡單系統運動與線性反應擴散方程混沌復雜性研究

報告摘要: 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.

報告時間：2025年3月17日（周一）上午9:00-10:30

報告地點：線上，騰訊會議：292-780-317

報告人簡介：

楊啟貴，理學博士，二級教授，博士生導師，華南理工大學教學名師。主要從事微分方程幾何理論、混沌動力系統、隨機動力系統及其應用的研究與教學工作，研究系統簡單到何種程度仍然具有混沌復雜性，揭示混沌系統混沌機理與復雜動力學特征。 曾獲廣西科技進步一等獎(排名：1/4)和廣東省高等教育省級教學成果二等獎(排名：2/5)，連續3次廣東省優秀博士論文指導教師等。至今為止，國內外發表論文150多篇，SCI正面他引2800多次。主持多項國家和省部級項目。已培養出站博士后5人、畢業博士25人（其中2名留學生）、碩士38人，現在讀博士生5人和碩士生6人。