报告题目1：A Dynamical System‑Based Approach to Identifying Slow‑Fast Relaxation Oscillations

报告人：郁培教授，加拿大西安大略大学

报告时间：2026年5月29日（周五）18:40-21:40

报告地点：20-306

报告摘要：An early‑developed simple criterion was employed to detect the existence of slow‑fast relaxation oscillations arising in differential systems for which geometric singular perturbation theory (GSPT) is inapplicable. In this talk, we present several models that violate these conditions yet still exhibit recurrent behavior. Such observations motivate us to generalize the original conditions, formulate new straightforward hypothetical criteria for identifying slow‑fast relaxation oscillations, and lay groundwork toward developing a rigorous mathematical theory.

报告人简介：郁培于1982年获得上海交通大学学士学位，分别于1984年和1986年加拿大滑铁卢大学获硕士和博士学位，现任加拿大西安大略大学应用数学系教授、博导。郁教授是常微分方程与动力系统领域著名专家，在微分方程定性、分支理论等方面做出了杰出的工作，曾获安大略省长杰出研究奖，在SIAM Review，SIAM 数学系列，JDE，JNS，Physica D等杂志上已发表300余篇论文，在Springer等出版社出版多部专著，担任多个国际知名杂志编委。

报告题目2：On spectral theory of singular Hamiltonian systems

报告人：孙华清教授，江苏师范大学

报告时间：2026年5月29日（周五）18:40-21:40

报告地点：20-306

报告摘要：This talk is concerned with essential spectra and essential numerical ranges of Hamiltonian systems with one singular endpoint. Characterizations of each element of the essential spectrum are established, and the corresponding perturbation theory for essential spectra, as well as for essential numerical ranges, are given.

报告人简介：孙华清，江苏师范大学，教授、博士生导师，一直从事奇异微分与差分算子谱理论研究，在J. Funct. Anal.，J. Differential Equations，Proc. Roy. Soc. Edinburgh Sect. A，Math. Nachr等国际权威杂志上发表30多篇SCI收录的论文，先后获国家自然科学基金以及其他省部级项目多项。

报告题目3：Melnikov analysis in the complex cubic-quintic Ginzburg-Landau equation with higher-order dispersion

报告人：孙宪波教授，杭州师范大学

报告时间：2026年5月29日（周五）18:40-21:40

报告地点：20-306

报告摘要：In this paper, we study periodically amplitude-modulated waves in the complex cubic-quintic Ginzburg-Landau equation with higher-order dispersion through local and global Melnikov analysis. A novel feature is to construct the displacement map on an integrable structure by transforming the infinite-dimensional equation into a near-Hamiltonian dynamical system on an invariant two-dimensional flow. Our analysis reveals the existence of periodically amplitude-modulated waves by investigating degenerate Hopf bifurcation, heteroclinic bifurcation, and Poincaré bifurcation in the near-Hamiltonian system. These bifurcation analyses illuminate the transition from stationary plane waves to periodically amplitude-modulated waves, including the waves with small, medium and large amplitudes, as well as the establishment of an upper sharp bound on these periodic waves under a given set of equation coefficients. The mathematical techniques are selected from the research on the weak Hilbert’s 16th problem.

报告人简介：孙宪波，教授，博士毕业于西安大略大学，主要从事弱化希尔伯特第十六问题相关研究及其方法应用。在Journal of Differential Equations, Physica D, Chaos, Journal of Symbolic Computation, Bulletin des Science Mathematique，《中国科学》等期刊发表学术论文40余篇；主持国家自然科学基金4项（面上1项，青年1项，地区2项），主持省部级项目3项；杭州市C类人才。

邀请人：动力系统与非线性分析研究所