报告题目：Analysis of Enzyme-Catalyzed Reaction Model报告时间：2015年11月7日下午15：30报告地点：数学馆310报告人：四川大学 张伟年教授报告摘要：In this talk we discuss a substrate-activator system, which depends on a cubic polynomial with such a complicated relation between its coefficients and the original parameters that the coordinates of equilibria or even the number of equilibria can hardly be determined in many cases. All found results on its qualitative properties and bifurcations are given indirectly for the artificial parameter s_*, a coordinate of a general equilibrium, and the analysis of its dynamics remains far from completion. Not following the common idea of computing eigenvalues at equilibria, we give a complete analysis of equilibria directly for those original parameters by using continuity, monotonicity and some techniques of inequality. For a global analysis we discuss its equilibria at infinity, one of which possesses degeneracy so high sometimes that neither the well known normal sector method nor the blowing-up method can be used easily. Furthermore, overcoming those difficulties from not solving all coordinates of equilibria, we give a versal unfolding with its original parameters to the degenerate cases and present bifurcation curves of periodic orbits and homoclinic orbits explicitly.专家简介：张伟年，四川大学数学学院教授，博士生导师，国家杰出青年基金获得者，主持完成多项国家自然科学基金项目。张伟年教授长期从事微分方程与动力系统的理论研究和应用，包括微分方程形式的连续型动力系统和差分迭代形式的离散动力系统。曾应邀到英国华威大学、加拿大滑铁卢大学、法国南特中央大学等讲学或开展科研合作。在国家核心和国际学术期刊上已发表学术论文100余篇，其中SCI收录80余篇，包括在英国《非线性》、美国《微分方程杂志》、美国《SIAM科学计算》等等。同时还获得“中国青年科技奖”、教育部“高校青年教师奖”、教育部“中国高校科学技术奖”、“国家教学成果二等奖”，获国务院颁发“政府特殊津贴”，四川省“学术与技术带头人”和四川省“教学名师奖”。