广州数学大讲坛第六期

第五十四讲—中北大学罗晓峰副教授学术报告

题目：Pattern emergence and optimal control in networked reaction–diffusion systems

时间：11月6日（周五）下午15：30

地点：计算机实验楼718

报告人：罗晓峰 副教授

摘要：Localized oscillations confined to network subsets appear in neural, ecological, and chemical systems. While prior work links them to wave bifurcations (oscillatory Turing instabilities) requiring at least three interacting components, we propose an alternative mechanism: a Hopf-type instability acting on a subcritical Turing branch, which works with just two components. We confirm its robustness in Brusselator and FitzHugh–Nagumo models on Barabási–Albert, Erdős–Rényi, and Watts–Strogatz networks, extending the generality of such patterns. Building on this, we introduce a control scheme to steer networked reaction–diffusion systems toward any desired dynamics. Our method extends to simplicial complexes, collapsed into weighted networks via linear Laplacian relations, and combines reaction and diffusion controls. It outperforms traditional single-variable control in both effectiveness and cost. Numerical tests on FitzHugh–Nagumo and SIR models demonstrate its resilience across systems. Together, our work offers both a new understanding of localized pattern formation and a practical tool for managing collective dynamics in complex networks.

报告人简介：

罗晓峰，中北大学数学杏吧传媒 副教授，数学与应用数学系副主任，博士生导师，入选国家自然科学基金天元数学西部地区优秀青年人才培育计划，山西省青年拔尖人才(山西省高层次人才D类)，CSIAM第三届数学生命科学专委会委员，中国数学会第九届生物数学专业委员会青年工作委员会委员；主要从事生物数学、网络传染病动力学、网络斑图动力学以及传染病最优防控策略的研究，在Natl. Sci. Rev.、Phys. Rep.、J. Math. Biol.、B. Math. Biol.、Phys. Rev. Research等国内外重要学术期刊发表论文40余篇。主持国家自然科学基金面上项目、国家自然科学基金青年基金项目(C类)，山西省基础研究计划青年基金项目等，参与科技部重大专项课题1项，获山西省自然科学一等奖1项。