学术活动

四川大学数学学院院长、国家杰青张伟年教授应邀来我校讲学

作者: | 来源:数学学院 | 发布日期:2019-04-03

题目:Analysis of Enzyme-Catalyzed Reaction Model
时间:2019年4月6日上午10:00
地点:立志楼A422
主办:数学与计算科学学院
报告人简介:
       张伟年,四川大学数学学院教授,博士生导师,国家杰出青年科学基金获得者。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。主持国家自科基金多项,在英国《非线性》、美国《微分方程杂志》、美国《SIAM科学计算》等知名刊物上发表学术论文100余篇。多次应邀到加拿大滑铁卢大学、英国Warwick大学、 法国南特中央大学(Ecole Centrale Nantes)、Brigham Young大学等国外著名大学开展科研合作。曾担任过中国科学院成都计算所数理科学中心副主任; 中国科学中国科学院成都分院科技处处长,是美国数学会会员,美国《Mathematical Reviews》评论员。

        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 wellknown 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.
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