报告题目：The diffusion-driven instability and complexity for a single-handed discrete Fisher equation
报告人：张广 天津商业大学
报告时间：2019年4月12日(星期五)上午11:00-12:00
报告地点：数学院4楼425报告厅
内容摘要：It seems to be a necessary condition that the diffusion coefficient of the inhibitor must be larger than that of the activator when the Turing instability is considered. However, the diffusion-driven instability/Turing instability for a single-handed discrete Fisher equation with the Neumann boundary conditions may occur and a series of 2-periodic patterns have be observed. Motivated by these pattern formations, the existence of 2-periodic solutions is also established by using the inverse function theorem. Naturally, the periodic double and the chaos phenomenon should be considered. To this end, a simplest two elements system will be further discussed, the flip bifurcation theorem will be obtained by computing the center manifold, and the bifurcation diagrams will be simulated by using the shooting method. Thus, the Turing instability and the complexity of dynamical behaviors can be completely driven by the diffusion term. Additionally, those effective methods of numerical simulations are also valid for experiments of other patterns, thus, are beneficial for some application scientists.
报告人简介：张广，博士、教授、天津商业大学学术委员会委员、天津大学博士生导师、美国数学会会员、国际差分方程学会会员、DDNS（SCI收录期刊，JCR三区）编委。主要从事微分方程与动力系统研究，发表科研论文150余篇，出版专著2部。主持国家自然基金面上项目1项（2014-2017）。主持完成的项目获得省部级科技进步奖三等和二等奖各1次。曾受邀访问过台湾、智利、韩国、加拿大、英国等国家和地区。
