一、题目: Spatiotemporal dynamics in a diffusive mussel-algae model
二、主讲人：宋永利教授
三、时 间：2017年3月9日（周四），下午：16:00-16 40
四、地 点：闻理园A4-305室
报告摘要: Intertidal mussels often self-organizes into spatial patterns, range from centimeters to meters scales with the labyrinths, spots and stripe patterns. The leading explanations for these phenomenon are the reaction-diffusion-advection model and phase separation model. This paper is continued in the recent series studies on a analytical understanding of the existence on the reaction-diffusion mussel-algae model. The stability of the positive constant equilibrium, and the existence of Hopf and steady state bifurcations are studied by analyzing the corresponding characteristic equation. Furthermore, we focus on the Turing-Hopf bifurcation and obtain the explicit dynamical classification in the neighborhood of the Turing-Hopf bifurcation point by calculating and investigating the normal form on the center manifold. We demonstrates via theoretical and numerical simulations that the reaction-diffusion mussel-algae model significantly enhances the diversity of spatial patterns, where the temporal oscillation with spatial homogeneous patterns, spatial oscillation with temporal static patterns, and both temporal and spatial oscillation patterns would be well understand with interactions of the Turing-Hopf bifurcation.
报告人简介：宋永利，杭州师范大学特聘教授，博士生导师。2011年入选教育部新世纪优秀人才计划。2005年毕业上海交通大学数学系获理学博士学位。现为国际学术期刊APM和TMA编委。长期从事时滞微分方程分支理论、混沌控制、神经网络的动力学、时滞耦合系统的稳定性及同步模式、生物系统中的图灵模式等方面的研究工作。已在《Journal of Nonlinear Science》、《Physica D》、《Nonlinearity》等国际学术期刊上发表学术论文60余篇。2014年, 2015年，2016年连续三年入选中国高被引学者(Most Cited Chinese Researchers)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、上海市创新项目等十余项。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。
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非线性研究团队
2017年3月6日
