广州数学大讲坛第六期

第五十三讲—南开大学柳迪副教授学术报告

题目：Dynamics of a nonlocal aggregation-diffusion model with spatial memory

时间：11月6日（周五）下午14：30

地点：计算机实验楼718

报告人：柳迪 副教授

摘要：We investigate a one-dimensional nonlocal reaction–diffusion–aggregation system coupled with a dynamically evolving spatial map that captures the effects of spatial perception and memory on population movement. Using an iterative approach, we establish the existence and uniqueness of global weak solutions. We then analyze the spectral properties and stability of the homogeneous steady state, derive critical bifurcation thresholds, and characterize the existence, direction, and stability of nonconstant steady states arising through pitchfork bifurcations. In particular, we reveal that the symmetry and asymmetry of the spatial kernel lead to fundamentally different dynamical behaviors, highlighting the crucial role of kernel structure in determining system stability and pattern formation.

报告人简介：

柳迪，南开大学数学科学91论坛副教授。研究方向是微分方程与动力系统，主要研究生物数学中种群模型的动力学行为。研究成果发表在J. Differential Equations，J. Nonlinear Sci.，Physica D等国际知名学术期刊上。主持国家自然科学基金青年科学基金项目，中国博士后科学基金特别资助项目及中国博士后科学基金面上项目。