报告题目1：Bifurcation of limit cycles for piecewise perturbations of some Hamiltonian systems

报告人：田云教授，上海师范大学

报告时间：2026年7月3日（周五）13:00-18:00

报告地点：20-308

报告摘要：In this talk, we derive the sharp upper bound on the number of isolated zeros of Melnikov function near a homoclinic or heteroclinic loop for cubic piecewise perturbations of the elliptic Hamiltonian $H(x,y)=1/2y^2 + 1/2x^2 + (a+1)/3x^3 + a/4x^4$, where $a \neq 0$ is a free parameter. Picard-Fuchs equations are applied to recursively compute the coefficients of the asymptotic expansion of Melnikov function.

报告人简介：田云，上海师范大学数学系教授，博士生导师，博士毕业于加拿大西安大略大学应用数学系，从事常微分方程定性理论、计算机符号等方向的研究，在JDE等学术期刊上发表论文30余篇。

报告题目2：Homoclinic bifurcation and Poincaré bifurcation within the normally hyperbolic manifold for a hydrodynamic singularly peterbed boussinesq equation

报告人：孙宪波教授，杭州师范大学

报告时间：2026年7月3日（周五）13:00-18:00

报告地点：20-308

报告摘要：We investigate the existence and multiplicity of periodic travelingwaves in a fifth-order singularly perturbed Boussinesq equation incorporatingboth Stokes (linear) damping and hydrodynamic (nonlinear) damping. Thecoexistence of dissipative terms and fifth-order odd dispersion breaks the integrable Hamiltonian structure of the classical Boussinesq equation and destroysthe symplectic invariance of the traveling-wave reduction, rendering standardvariational and PDE methods inapplicable. By reducing the PDE via geometricsingular perturbation theory (GSPT) to a near-Hamiltonian system on anormally hyperbolic invariant slow manifold, we uncover three distinct geometricbifurcation mechanisms governing the emergence of multiple periodic travelingwaves: degenerate Hopf bifurcation (small-amplitude waves from localdegeneration of elliptic leaves), homoclinic bifurcation (large-amplitude wavesfrom global separatrix splitting), and Poincaré bifurcation (waves throughoutthe period annulus from selective persistence of invariant leaves). A combinedgeometric-algebraic framework is developed to overcome the difficulty of analysing Melnikov functions with multiple generating elements for higher-degree Hamiltonian systems in the Poincaré bifurcation study. Rigorous bounds onthe maximal number of periodic traveling waves are established, and numericalsimulations corroborate the theoretical findings.

报告人简介：孙宪波，杭州师范大学教授，博士生导师。博士毕业于韦仕敦大学；在Journal of Differential Equations, Physica D, Chaos, Journal of Symbolic Computation, Bulletin des Science Mathematique，《中国科学》等期刊上发表学术论文40余篇；主持国家自然科学基金项目4项（面上1项，青年1项，地区2项），主持省部级项目3项。

报告题目3：On Some Cases of Zoladek-Iliev's Conjecture

报告人：孙杨剑副教授，上饶师范学院

报告时间：2026年7月3日（周五）13:00-18:00

报告地点：20-308

报告摘要：Zoladek and Iliev proposed an important conjecture on the cyclicity of a period annulus of quadratic reversible system under quadratic perturbations: the bifurcation functions corresponding to quadratic centers satisfy either the Chebyshev property or the Chebyshev property with accuracy 1. In this paper, we adopt the criterion function method and the real root isolation algorithm for multivariate polynomial systems to prove that, for five cases of generic quadratic reversible systems whose first integrals contain the logarithmic function, the cyclicity of each period annulus is 2. This result indicates that the corresponding bifurcation functions satisfy the Chebyshev property and this conjecture holds for these quadratic reversible systems. The present work is a joint effort with Cen Xiuli, Chen Shangming, and Ji Guilin.

报告人简介：孙杨剑，博士，上饶师范学院数计学院副教授，主要从事常微分方程定性理论的研究。目前主持国家自然科学基金青年项目1项，在Science.China. Math、Proce.Roya.Soc.Edinb.Soc、Physica D、Bull.Sci.Math.等期刊上发表高水平论文10余篇。

报告题目4：非光滑微分系统的平均法和Melnikov函数法之间的等价性问题

报告人：可爱，东华大学

报告时间：2026年7月3日（周五）13:00-18:00

报告地点：20-308

报告摘要：已知在研究平面光滑微分系统的极限环个数时，利用平均法和Melnikov函数法得到的结果是等价的。本次报告内容将结合已有的文献成果，进一步探究两类方法在平面非光滑微分系统中的等价性关系。

报告人简介：可爱，东华大学讲师，博士毕业于上海师范大学，曾在浙江师范大学从事博士后工作，现主要从事微分方程与动力系统研究。在Journal of Differential Equations、Qualitative Theory of Dynamical Systems、Physica D、International Journal of Bifurcation and Chaos等国际SCI期刊上发表论文多篇，主持国家自然科学基金青年项目1项（2024年1月—2026年12月）。

报告题目5：Averaging method of piecewise smooth systems

报告人：刘姗姗，福建师范大学

报告时间：2026年7月3日（周五）13:00-18:00

报告地点：20-308

报告摘要：In this talk, we introduce the bifurcation methods of limit cycles for piecewise smooth systems. We concern the Melnikov function method and averaging method of perturbed piecewise integrable systems in arbitrary dimension, and establish a relationship between them by Poincare map.

报告人简介：刘姗姗，福建师范大学数学与统计学院讲师，主要从事常微分定性理论的研究工作，特别是对弱化的Hilbert第16问题、同宿异宿极限环分支等相关问题的研究。在 J. Differential Equations、Chaos Solitons Fractals、Comput. Appl. Math.、Bull. Sci. Math.等期刊上发表过多篇论文。

邀请人：动力系统与非线性分析研究所