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A New Approach to Synchronization Analysis of Linearly Coupled Map Lattices

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Chinese Annals of mathematics,Series B 2007年第2期28卷 149-160页

作者： Wenlian LU Tianping CHENt Published online March School of Mathematical sciences and laboratory of {2. for nonlinear sciences Fudan University Shanghai 200433 China.

In this paper, a new approach to analyze synchronization of linearly coupled map lattices （LCMLs） is presented. A reference vector x（t） is introduced as the projection of the trajectory of the coupled system on the synchronization manifold. The stability analysis of the synchronization manifold can be regarded as investigating the difference between the trajectory and the projection. By this method, some criteria are given for both local and global synchronization. These criteria indicate that the left and right eigenvectors corresponding to the eigenvalue ＂0＂ of the coupling matrix play key roles in the stability of synchronization manifold for the coupled system. Moreover, it is revealed that the stability of synchronization manifold for the coupled system is different from the stability for dynamical system in usual sense. That is, the solution of the coupled system does not converge to a certain knowable s（t） satisfying s（tT1） = f（s（t）） but to the reference vector on the synchronization manifold, which in fact is a certain weighted average of each x^i（t） for i=1,……, m, but not a solution s（t） satisfying s（t ＋ 1）=f（s（t））.

关键词： Linearly coupled map lattices Synchronization Synchronizationmanifold Local stability of synchronization manifold Global stability of synchronization manifold

Limit theorem and uniqueness theorem of backward stochastic differential equations

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Science china mathematics 2006年第10期49卷 1353-1362页

作者： JIANG Long Department of mathematics, china {2. of Mining and Technology, Xuzhou 2.1008, china institute of mathematics, fudan university, shanghai 200433, china School of mathematics and System sciences, Shandong {2., Jinan 2.0100, china Department of mathematics China University of Mining and Technology Xuzhou China institute of mathematics Fudan University Shanghai China School of mathematics and System sciences Shandong University Jinan China

This paper establishes a limit theorem for solutions of backward stochastic differential equations (BSDEs). By this limit theorem, this paper proves that, under the standard assumption g(t,y,0) = 0, the generator g of a BSDE can be uniquely determined by the corresponding g-expectationεg;this paper also proves that if a filtration consistent expectation S can be represented as a g-expectationεg, then the corresponding generator g must be unique.

关键词： backward stochastic differential equation, g-expectation, generator.

On the Neighborhood in Stabilizing Period-T Orbits for Chaotic m Degree Polynomial Dynamical System

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Communications in nonlinear Science and Numerical Simulation 1998年第4期3卷 242-247页

作者： Enguo GU Jiong RUAN and Zhenxun HUANG (institute of mathematics,{2., shanghai 200433,china) institute of mathematics Fudan University Shanghai 200433 China

In this paper, a problem of stabilizing a period-T orbit in discrete Chaotic m degree polynomial dynamical systems is studied. The aim is to present a new method for determining the neighborhood of a period-T point in which the system remains stable when subjected to a linear feedback control. A theorem on the existence of neighborhood is rigorously proved using idea from functional analysis and polar coordinate *** ways of implementing the obtained theorem in the Henon map are proposed. Thevalidity of this method is shown by numerical simulation.

关键词： neighborhood of period-T orbit controlling chaotic discrete system gain matrix

A maximum principle for optimal control problem of fully coupled forward-backward stochastic systems with partial information

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Science china mathematics 2009年第7期52卷 1579-1588页

作者： MENG QingXin1,2.1 Department of Mathematical sciences,Huzhou university,Zhejiang 313000,{2. 2.institute of mathematics,fudan university,shanghai 200433,{2. Department of Mathematical sciences Huzhou University Zhejiang China institute of mathematics Fudan University Shanghai China

The paper is concerned with a stochastic optimal control problem in which the controlled system is described by a fully coupled nonlinear forward-backward stochastic differential equation driven by a Brownian *** is required that all admissible control processes are adapted to a given subfiltration of the filtration generated by the underlying Brownian *** this type of partial information control,one sufficient(a verification theorem) and one necessary conditions of optimality are *** control domain need to be convex and the forward diffusion coefficient of the system can contain the control variable.

关键词： maximum principle stochastic optimal control partial information 93E2. 60H10 60H30

ALMOST GLOBAL EXISTENCE OF DIRICHLETINITIAL-BOUNDARY VALUE PROBLEM FORnonlinear ELASTODYNAMIC SYSTEMOUTSIDE A STAR-SHAPED DOMAIN

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Chinese Annals of mathematics,Series B 2004年第4期25卷 433-454页

作者： XINJIE QINTIEHU instituteofmathematics FudanUniversityShanghai200433China Departmentofmathematics FudanUniversityShanghai200433China

This paper deals with the mixed initial-boundary value problem of Dirichlet type for the nonlinear elastodynamic system outside a star-shaped domain. The almost global existence of solution with small initial data to ... 详细信息

关键词： nonlinear elastodynamic system Exterior problem Almost global existence

On Galois Extension of Hopf Algebras

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Chinese Annals of mathematics,Series B 2008年第1期29卷 65-70页

作者： Guohua LIU Shenglin ZHU Department of mathematics Southeast University Nanjing 210096 China Key laboratory of mathematics for {2. sciences School of Mathematical Sciences Pudan University Shanghai 200433 China

Let H be a cosemisimple Hopf algebra over a field k, and π ： A→ H be a surjective cocentral bialgebra homomorphism of bialgebras. The authors prove that if A is Galois over its coinvariants B=LH Ker π and B is a sub-Hopf algebra of A, then A is itself a Hopf algebra. This generalizes a result of Cegarra [3] on group-graded algebras.

关键词： Hopf algebra Galois extension

The rate of convergence of the Lax-Oleinik semigroup-degenerate fixed point case

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Science china mathematics 2011年第3期54卷 545-554页

作者： WANG KaiZhi1,2.& YAN Jun1 1School of Mathematical sciences and Key Lab of mathematics for {2. Science, fudan university, shanghai 200433, china 2.chool of mathematics, Jilin university, Changchun 130012. china School of Mathematical sciences and Key Lab of mathematics for {2. Science Fudan University Shanghai China School of mathematics Jilin University Changchun China

For the standard Lagrangian in classical mechanics, which is defined as the kinetic energy of the system minus its potential energy, we study the rate of convergence of the corresponding Lax-Oleinik semigroup. Under the assumption that the unique global minimum point of the Lagrangian is a degenerate fixed point, we provide an upper bound estimate of the rate of convergence of the semigroup.

关键词： Hamiltonian system weak KAM theorem Lax-Oleinik semigroup

Global Exact Boundary Controllability for Cubic Semi-linear Wave Equations and Klein-Gordon Equations

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Chinese Annals of mathematics,Series B 2010年第1期31卷 35-58页

作者： Yi ZHOU Wei XU Zhen LEI Key laboratory of mathematics for {2. sciences School of Mathematical Sciences Fudan University Shanghai 200433 China School of Mathematical sciences Fudan University Shanghai 200433 China

The authors prove the global exact boundary controllability for the cubic semilinear wave equation in three space dimensions,subject to Dirichlet,Neumann,or any other kind of boundary controls which result in the well-posedness of the corresponding initial-boundary value *** exponential decay of energy is first established for the cubic semi-linear wave equation with some boundary condition by the multiplier method,which reduces the global exact boundary controllability problem to a local *** proof is carried out in line with [2.15].Then a constructive method that has been developed in [13] is used to study the local *** when the region is star-complemented,it is obtained that the control function only need to be applied on a relatively open subset of the *** the cubic Klein-Gordon equation,similar results of the global exact boundary controllability are proved by such an idea.

关键词： Global exact boundary controllability Cubic semi-linear wave equations The exponential decay Star-shaped Star-complemented Cubic Klein- Gordon equations

Riemann boundary value problems and reflection of shock for the Chaplygin gas

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Science china mathematics 2012年第4期55卷 671-685页

作者： CHEN ShuXing 1,& QU AiFang 2.1 School of Mathematical sciences,fudan {2.,shanghai 200433,china 2.Wuhan institute of Physics and mathematics,Chinese Academy of sciences,Wuhan 430071,china School of Mathematical sciences Fudan University Shanghai China Wuhan institute of Physics and mathematics Chinese Academy of Sciences Wuhan China

In this paper,we study two-dimensional Riemann boundary value problems of Euler system for the isentropic and irrotational Chaplygin gas with initial data being two constant states given in two sectors respectively,where one sector is a quadrant and the other one has an acute vertex *** prove that the Riemann boundary value problem admits a global self-similar solution,if either the initial states are close,or the smaller sector is also near a *** result can be applied to solving the problem of shock reflection by a ramp.

关键词： Riemann boundary value problem reflection of shock Chaplygin gas wave interaction Eulersystem