报告题目1：Latest studies on ion channel problems via Poisson-Nernst-Planck models

报告人：张明吉教授，美国新墨西哥矿业理工学院

报告时间：2024年6月13日（周四）9:00-10:00

报告地点：20-200

报告摘要：We briefly introduce some latest results of our studies on related ion channel problems. We mainly focus on the dynamics of ionic flows through membrane channels via Poisson-Nernst-Planck models under different setups, particularly the internal dynamics, which cannot be detected via current technology. More precisely, the characterization of the nonlinear interplays between different physical parameters, particularly, boundary conditions, finite ion sizes, permanent charges, diffusion coefficients and channel geometry, is our main focus. This provides detailed information and better understandings for the ionic flow properties of interest.

报告人简介：张明吉，美国新墨西哥矿业理工学院数学系教授。2013年毕业于美国堪萨斯大学，获理学博士学位；2013至2015年跟随Peter Bates教授在密歇根州立大学做博士后研究，研究领域是非线性动力系统、微分方程及其应用。目前研究主要侧重于(1)几何奇异摄动理论及其应用, 特别是在离子通道问题和发展生物学中的应用；(2)非线性偏微分方程的随机动力学研究。在J. Differential Equations、J. Dynamics and differential Equations、Nonlinearity、J. Nonlinear Science、SIAM J. Applied Mathematics、SIAM J. Applied Dynamical Systems等杂志发表相关学术论文近50篇。担任SIAM系列、DCDS系列等50余个国际SCI杂志的特约审稿⼈，美国《数学评论》评论员，德国《数学文摘》评论员。

报告题目2：Dynamics of slow-fast Leslie-Gower predator-prey systems

报告人：温振庶教授，华侨大学

报告时间：2024年6月13日（周四）10:00-11:00

报告地点：20-200

报告摘要：We transform Leslie-Gower predator-prey systems into the corresponding fast-slow versions by assuming that prey reproduces much faster than predator, and then focus on their dynamics. More specifically, we find the necessary and sufficient conditions of the exact number of positive equilibria of the slow-fast systems and its (or their) location, and then we further fully determine its (or their) dynamics under explicit conditions. Besides, by converting the slow-fast system into their slow-fast normal form, we are able to characterize their rich dynamics completely, including relaxation oscillation, singular Hopf bifurcation, canard explosion, homoclinic orbits, heteroclinic orbits, and global attraction of equilibrium. Moreover, the sufficient conditions to guarantee these various rich dynamics are explicitly given, including the explicit conditions to determine whether singular Hopf bifurcation is supercritical or subcritical, which generally cannot be explicitly derived in the existing literatures. Additionally, the cyclicity of diverse canard cycles is found under explicit conditions.

报告人简介：温振庶，华侨大学教授，从事微分方程与动力系统及其应用方面的研究。2012年于华南理工大学数学学院获理学博士学位。2018年，受国家留学基金资助，赴美国新墨西哥矿业理工学院访学一年。现主持国家自然科学基金面上项目1项。在Nonlinearity、Journal of Nonlinear Science、JDDE、Journal of the American Medical Informatics Association等SCI期刊发表论文40余篇。