无穷维动力系统会议
近年来，我们发现有限维微分动力系统中的一些想法和技巧正在越来越多地应用在由偏微分方程生成的一些无穷维动力系统中。但是其中似乎还有很大的值得探索的余地。
有鉴于此，我们觉得有必要组织一次学术活动来进行微分动力系统和无穷维动力系统的有效交流
会议将于2014年2月16日至2013年2月19日在威尼斯人-威尼斯人娱乐场
举办。本次参加会议的专家有上海师范大学蒋继发教授、中国科学技术大学王毅教授、苏州大学曹永罗教授以及杨大伟教授等。参加会议的还有一批其他活跃在科学研究前沿的青年学者。
主办单位：苏州大学
承办单位：威尼斯人-威尼斯人娱乐场
附学术报告安排：
报告题目： Comparison Theorem for Stochastic
Functional Differential Equations with
Application to Delayed Hopfield Neural
Network Model （I）
报告人：蒋继发教授（上海师范大学）
时间： 2014年2月17日（周一）下午 14:30 至 15:20
地点：学术报告厅
报告内容简介：The comparison theorem is proved for stochastic functional differential equations
(SFDEs) whose drift term satisfies the quasimonotone condition and diffusion term is
independent of delay. Meanwhile, it is proved that a system of random functional dif-
ferential equations (RFDEs), satisfying global Lipschitz condition, generates a random
dynamical system (RDS). Applying these results to delayed Hopfield neural network
model with multiplicative noise, we get that it generates a RDS. If the connection ma-
trix is positive and activation functions are sublinear, then it generates a sublinear
order-preserving RDS, therefore, it has a trichotomy dynamics.
报告题目： Stability of Nonlinear Dirac Solitary Waves
报告人：邵嗣烘（北京大学副教授）
时间： 2014年2月17日（周二）上午 15：30 至 16:20
地点：学术报告厅
报告内容简介：
In this talk, we first present a brief introduction to the nonlinear Dirac equation and then raise the stability issue of its solitary wave solutions from several new numerical observations. Using the exact analytic form for
rest frame solitary waves, we study their stability numerically and discuss the validity
of various approaches to understand the stability that were successful in the nonlinear SchrÖdinger equation.
In particular we study the validity of a version of Derrick's theorem,
the criterion of Bogolubsky as well as the Vakhitov-Kolokolov criteria. Further remarks and future directions are also presented.
rest frame solitary waves, we study their stability numerically and discuss the validity
of various approaches to understand the stability that were successful in the nonlinear SchrÖdinger equation.
In particular we study the validity of a version of Derrick's theorem,
the criterion of Bogolubsky as well as the Vakhitov-Kolokolov criteria. Further remarks and future directions are also presented.
题目：无穷维动力系统中的指数分离性及应用
报告人：王毅（中国科大教授）
时间： 2014年2月18日（周二）上午 09:30 至 10:20
地点：学术报告厅
摘要：我们首先说一些PDE转换成无穷维动力系统的例子，介绍无穷维系统不变流形的最简单的情形及证明；其次引入无穷维系统不变集的指数分离性，并介绍在此假设下，已有的相关不变流形的结论及应用。
报告题目： Comparison Theorem for Stochastic
Functional Differential Equations with
Application to Delayed Hopfield Neural
Network Model （II）
报告人：蒋继发教授（上海师范大学）
时间： 2014年2月18日（周二）上午 10:30 至 11:20
地点：学术报告厅
报告内容简介：The comparison theorem is proved for stochastic functional differential equations
(SFDEs) whose drift term satisfies the quasimonotone condition and diffusion term is
independent of delay. Meanwhile, it is proved that a system of random functional dif-
ferential equations (RFDEs), satisfying global Lipschitz condition, generates a random
dynamical system (RDS). Applying these results to delayed Hopfield neural network
model with multiplicative noise, we get that it generates a RDS. If the connection ma-
trix is positive and activation functions are sublinear, then it generates a sublinear
order-preserving RDS, therefore, it has a trichotomy dynamics.
报告题目： The integrability on dominated splitting
报告人：何宝林（北京国际数学中心博士后）
时间： 2014年2月18日（周三）上午 10：30 至 11:30
地点：学术报告厅
报告内容简介：we construct diffeomorphism on 2-torus with the dominated splitting E +F such that its splitting are robustly non-integrable
2.题目: Homoclinic Orbits for NLS with Spatially-Dependent and Unbounded Perturbations
报告人：王毅（中国科大教授）
时间： 2014年2月18日（周三）下午 14:30 至 15:20
地点：学术报告厅
摘要： For an integrable focusing cubic nonlinear Schrodinger equation (NLS) under spatial periodic boundary conditions, it is known that there are whiskered tori which form homoclinic orbits to periodic orbits with different asymptotic phases as time approaches plus and minus infinity. In this talk, we consider the integrable NLS under diffusive (unbounded) perturbation and spatially dependent time periodic forcing and show (based on singular perturbation method) that there exist orbits homoclinic to some saddle points. We note that as the normally elliptic invariant slow manifold does not necessarily persist under the spatially-dependent forcing, we need to apply a modified averaging technique to obtain a sufficiently accurate approximate invariant slow manifold. This is joint work with Shui-Nee Chow (GT) and Chongchun Zeng (GT).