报告题目：Spatiotemporal dynamics of the diffusive mussel-algae model near Turing-Hopf bifurcation

报告人：宋永利 教授 杭州师范大学
    邀请人：常永奎 教授、吴事良 教授
    报告时间：2018年4月20日(周五)10:30-11:30

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报告人简介： 2005 年于上海交通大学获博士学位，先后在同济大学和杭州师范大学工作。2011 年起任同济大学博士生指导教师。曾出访西班牙、澳大利亚、加拿大、美国做博士后或合作研究。现为两个国际学术期刊编委。主要从事无穷维动力系统的分支理论及应用、生物数学等方面的研究工作,已在Jounal of Differntial Equations,Journal of Nonlinear Science、 IEEE Transactions on Neural Networks and Learning Systems、Physica D、Nonlinearity 等国际学术期刊上发表学术论文60余篇，其中SCI收录50余篇。2014年起连续三年入选中国高被引学者榜单(数学类)。曾主持、或作为项目组主要成员参与完成国家自然科学基金重点项目、面上项目、上海市自然科学项目等十余项。目前正在主持一项国家自然科学基金面上项目的研究工作。2011年入选教育部新世纪优秀人才计划。

报告摘要：Intertidal mussels can self-organize into periodic spot, stripe, labyrinth and gap patterns range from centimeters to meters scales. The leading mathematical explanations for these phenomena are the reaction-diffusion-advection model and phase separation model. This paper is continued in the series studies on analytical understanding of the existence of pattern solutions in the reaction-diffusion mussel-algae model. The stability of the positive constant steady state, the existence of Hopf and steady state bifurcations are studied by analyzing the corresponding characteristic equation. Furthermore, we focus on the Turing-Hopf (TH) bifurcation and obtain the explicit dynamical classification in its neighborhood by calculating and investigating the normal form on the center manifold. Using theoretical and numerical simulations, we demonstrates that this TH interaction would significantly enhance the diversity of spatial patterns and trigger the alternative paths for the patterns development.

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