簡(jiǎn)單系統(tǒng)運(yùn)動(dòng)與線性反應(yīng)擴(kuò)散方程混沌復(fù)雜性研究

報(bào)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(bào)告時(shí)間：2025年3月17日（周一）上午9:00-10:30

報(bào)告地點(diǎn)：線上，騰訊會(huì)議：292-780-317

報(bào)告人簡(jiǎn)介：

楊啟貴，理學(xué)博士，二級(jí)教授，博士生導(dǎo)師，華南理工大學(xué)教學(xué)名師。主要從事微分方程幾何理論、混沌動(dòng)力系統(tǒng)、隨機(jī)動(dòng)力系統(tǒng)及其應(yīng)用的研究與教學(xué)工作，研究系統(tǒng)簡(jiǎn)單到何種程度仍然具有混沌復(fù)雜性，揭示混沌系統(tǒng)混沌機(jī)理與復(fù)雜動(dòng)力學(xué)特征。 曾獲廣西科技進(jìn)步一等獎(jiǎng)(排名：1/4)和廣東省高等教育省級(jí)教學(xué)成果二等獎(jiǎng)(排名：2/5)，連續(xù)3次廣東省優(yōu)秀博士論文指導(dǎo)教師等。至今為止，國內(nèi)外發(fā)表論文150多篇，SCI正面他引2800多次。主持多項(xiàng)國家和省部級(jí)項(xiàng)目。已培養(yǎng)出站博士后5人、畢業(yè)博士25人（其中2名留學(xué)生）、碩士38人，現(xiàn)在讀博士生5人和碩士生6人。