报告题目：Isolated periodic wave solutions arising from Hopf and Poincaré bifurcations in a class of single species model.

报告人：王勤龙 教授（桂林电子科技大学）

报告时间： 2022 年 05 月 28 日（周六） 19:00-20:00

腾讯会议号：782-453-726

校内联系人：衣凤岐 教授    联系电话：84708351-8118

报告摘要: In this talk, I will report our recent works on the bifurcations of local and global isolated periodic traveling waves in a single species population model described by a reaction-diffusion equation. Based on the singular point quantity algorithm of conjugate symmetric complex systems, we investigate Hopf bifurcation from all equilibrium points for the corresponding planar traveling wave system. We obtain all center conditions and construct one perturbed Hamiltonian system to study Poincaré bifurcation. Further, using the Chebyshev criterion, we develop a utilized approach to prove the existence of at most two limit cycles in a piecewise continuous parameter interval. Finally, the existence of double isolated periodic traveling waves for the model is established, and the results are illustrated by numerical simulation. It is shown that in a population model with density-dependent migrations and Allee effect, two large amplitude oscillations (isolated periodic traveling waves) can exist simultaneously. This is a joint work with Pei Yu and Wentao Huang.

报告人简介：王勤龙，教授，理学博士。现任职于桂林电子科技大学数学与计算科学学院，主要从事微分模型动力学性质的研究。2010年于美国加州大学（河滨）访学一年，2016年于英国莱斯特大学等访学2月。近来主持国家基金与广西基金项目各2项。在《Bulletin des Sciences Mathematiques(法国数学通报)》、《Journal of Differential Equations》、《数学学报（英文版）》等刊物上发表论文40余篇；一些研究结果，如所提出了三维系统焦点量线性化递推算法，得到了国际知名专家Valery G. Romanovsky和Colin J. Christopher等的好评；2016年主持获得广西自然科学奖三等奖1项。