题 目：Bifurcation and Its Normal Form of Reaction Diffusion Systems on Directed Networks

主讲人：靳祯

时 间：2024年5月9日（周四）下午14:30

地 点：#腾讯会议：544-601-971

主讲人简介：

靳祯 山西大学二级教授。现任教育部重点实验室主任，山西省数学会理事长，享受国务院政府特殊津贴。主要从事生物动力系统研究，先后主持国家自然基金项目10 项，其中国家基金重点项目2 项，国家重点研发计划子项目1项。曾获山西省科学技术奖（自然科学类）一等奖2项，教育部高等学校优秀成果二等奖奖（自然科学类）1项。

摘要：

Compared with the real Laplacian eigenvalues of undirected networks, the ones of asymmetrical directed networks might be complex, which is able to trigger additional collective dynamics, including the oscillatory behaviors. However, the high dimensionality of the reaction-diffusion systems defined on directed networks makes it difficult to do in-depth dynamic analysis. In this talk, we strictly derive the Hopf normal form of the general two-species reaction-diffusion systems defined on directed networks, with revealing some noteworthy differences in the derivation process from the corresponding on undirected networks. Applying the obtained theoretical framework, we conduct a rigorous Hopf bifurcation analysis for an SI reaction-diffusion system defined on directed networks, where numerical simulations are well consistent with theoretical analysis. Undoubtedly, our work will provide an important way to study the oscillations in directed networks.