【廿周年院庆学术报告86】·【和山数学论坛第372期】

一、报告题目: Turing instability and Hopf bifurcation of a spatially discretized diffusive Brusselator model with zero-flux boundary conditions

二、报告人：李遵先副教授

三、时 间：2023年6月10日（周六） 11:00-11:40

四、地 点：闻理园A4-218

报告摘要：A spatially discretized diffusive Brusselator model with zero-flux boundary conditions is considered. Firstly, the global existence and uniqueness of the positive solution are proved. Then the local stability of the unique spatially homogeneous steady state is considered by analyzing the relevant eigenvalue problem with the aid of decoupling method. Hence, the occurrence conditions of Turing bifurcation and Hopf bifurcation for the model at this steady state are obtained. Meanwhile, the comparative simulations on the stability regions of the steady state between the spatially discretized diffusive Brusselator model and its counterpart in continuous space are given. Furthermore, the approximate expressions of the bifurcating periodic solutions are derived according to Hopf bifurcation theorem. The bifurcating spatially nonhomogeneous periodic solutions show the formation of a special kind of periodic structures for this model. This is a joint work with Professors Song Yongli and Wu Chufen.

报告人简介：李遵先，天津理工大学副教授，研究方向：格微分方程和空间离散方程的动力学行为，包括其行波解、Turing失稳和Hopf分支等问题；在Nonl. Dyn.，Nonl. Anal.:RWA，IJBC， AMC， AMLetters，数学进展等杂志发表论文多篇，是Nonl. Anal.:RWA，IJBC，AMC，IJB等杂志的审稿人。

欢迎广大师生参加！ 联系人：李先义 ，韩仁基。