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常微分方程与动力系统的分支理论和应用
  • 项目名称：常微分方程与动力系统的分支理论和应用
  • 项目类别：重点项目
  • 批准号：10831003
  • 申请代码：A010703
  • 项目来源：国家自然科学基金
  • 研究期限：2009-01-01-2012-12-31
  • 项目负责人：李继彬
  • 负责人职称：教授
  • 依托单位：浙江师范大学
  • 批准年度：2008
中文摘要：

本项目涉及常微分方程与动力系统分支理论和应用方向的五个方面广义弱Hilbert第16问题，特别是可逆系统扰动问题的研究；等变动力系统的全局分支和非线性发展方程行波解的动力学性质和精确解研究；高次退化平衡点的普适开折、高余维数全局分支和生命科学中的非线性动力学模型研究；动力系统可积的代数、几何与拓扑性质、以及多项式微分系统的代数极限环研究；拓扑浑乱而统计平凡微分系统的遍历性质研究。这些课题是当前国际上常微分方程和动力系统研究的热门方向。 项目组全体成员力争在上述各个方向的研究中在理论和方法上作出创新性成果，以推动学科的发展。

中文主题词： 平面动力系统；非一致双曲系统动力学；非线性波方程；分支和混沌；流行病模型
英文摘要：

planar dynamical system；dynamics beyond uniform hyperb；nonlinear wave equation；bifurcation and Chaos；epidemiological model

英文主题词： planar dynamical system；dynamics beyond uniform hyperb；nonlinear wave equation；bifurcation and Chaos；epidemiological model
结论摘要：

项目组6名成员经4年研究, 获得的研究成果由在国际知名英文学术刊物(SCI检索)发表的学术论文94篇和在科学出版社出版的两本学术专著所组成. 项目组在平面向量场的经典问题研究方向获得系列新的国际先进结果, 解决了几个重要的公开问题; 在拓扑动力系统和微分动力系统方向, 在流的熵理论、奇异的SRB测度-非双曲的奇点测度、”走出一致双曲"的系统、光滑微分同胚在流中的嵌入的研究等方面获得令人关注的结果; 在奇非线性行波方程的动力学性质和精确解研究方向做出了独具特色的工作; 对高维系统或高余维退化系统的动力学复杂性和传染病的动力学的研究作出了新贡献. 培养了23名博士生, 35名硕士生; 项目组成员53人次在国际学术会议作报告. 一项成果获2011年度浙江省人民政府“浙江省科学技术奖”一等奖.

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  • 期刊论文
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期刊论文
某一类控制系统中发生的指数偏差现象
Extreme Growth Rates of Periodic Orbits in Flows
Riemann theta function periodic wave solutions for the variable- coefficient mKdV equation
Integrable discretizations and soliton solution of KdV and mKdV equations
Exact travelling wave solutions to two integrable KdV6 equations
Exact solitary wave and quasiperiodic wave solutions for four fifthorder nonlinear wave equations
Exact traveling wave solutions and bifurcations in a nonlinear elastic rod equation
A new Chebyshev family with applications to Abel equations
A note on “The integrable KdV6 equation: Multiple soliton solutions and multiple singular soliton so
Exact Travelling Wave Solutions and Their Bifurcations for the KudryashovSinelshchikov Equation
Metric entropy and the number of periodic points
On the travelling wave solutions for a nonlinear diffusionconvection equation: dynamical system appr
Lyapuniv exponents of hyperbolic measures and hyperbolic periodic orbits
A multiple exp- function method for nonlinear differential equations and its application
Hirota bilinear equations with linear subspaces of solutions
Exact heteroclinic cycle family and quasi-periodic solutions for the three-dimensional systems deter
Bifurcations and exact travelling wave solutions of the generalized twocomponent CamassaHolm equatio
Generalized Wronskian solutions for the (3 + 1)-dimensional Jimbo– Miwa equation
Uniqueness of limit cycles for Li\'enard differential equations of degree four
Knotted periodic solutions of a linear non-autonomous system and some related three- dimensional flo
Abelian integrals and limit cycles
Wronskian and Grammian Solutions for (2 + 1)-Dimensional Soliton Equation
Korteweg–de Vries Equation (KdV), History, Exact N- Soliton Solutions and Further Properties
Zero entropy versus infinite entropy
On the Hopf-zero bifurcation of the Michelson system
Homoclinic manifolds, center manifolds and exact solutions of fourdimensional travelling wave system
The embedding flows of C^\infty hyperbolic diffeomorphisms
Explicit soliton solutions of the Kaup-Kupershmidt equation through the dynamical system approach
Generalized rational first integrals of analytic differential systems
Bifurcation in a ratio-dependent predator-prey model with prey harvesting
The 16th Hilbert problem on algebraic limit cycles, Journal of Differential Equations
Global structure of quaternion polynomial differential equations
Solitary wave and chaotic behavior of travelling wave solutions for the coupled KdV equations
On nonlinear wave equations with breaking loop-solutions
Embedding smooth diffeomorphisms in flows
Soliton resonance of the NI-BKP equation
Non-uniformly hyperbolic periodic points and uniform hyperbolicity for $C^1$diffeomorphisms
New results on the study of $Z_q$-equivariant planar polynomial vector fields
Quadratic Perturbations of a Quadratic Reversible Lotka-Volterra System,
Bifurcations of traveling wave solutions of an integrable equation
Bifurcations and parametric representations of traveling wave solutions for the $(2+1)-$dimensional
On Dirac physical measures for transitive flows
Exact Dark Soliton, Periodic Solutions and Chaotic Dynamics in a Perturbed Generalized Nonlinear Sch
B?cklund transformations and soliton solutions for the KdV6 equation
Exact homoclinic orbits and heteroclinic families for the thirdorder system given by Chazy XI (N=3)
The exact bounds on the number of zeros of complete hyperelliptic integrals of the ?rst kind
Exact M/W-shape wave solutions determined by a singular traveling wave equation
Approximation properties on invariant measure and Oseledec splitting in non-hyperbolic systems
Exact dark soliton solution of the generalized nonlinear Schrdinger equation
Family of nonlinear wave equations which yield loop solutions and solitary wave solutions
On the Breaking Property for the Second Class of Singular Nonlinear Traveling Wave Equations
Limit cycles of differential systems via the averaging methods
Chaotic motion and Hamiltonian dynamics of a prestressed incompressible elastic plate due to resonan
A class of exact solutions of the generalized nonlinear Schrodinger equation
Exact loop solution,cusp solutions, solitary wave solutions and periodic wave solutions for the spec
The cyclicity of period annulus of a quadratic reversible Lotka-Volterra system, Nonlinearity
Resonance of solitons in a coupled higher-order Ito equation
Bounded complexity function versus unbounded complexity function
Canard Limit Cycles for Predator-Prey Systems with Holling Types of Functional Response
Exact Travelling Wave Solutions and Their Bifurcations for the generalized PochhammerChree equations
Exact solutions and Painlevé analysis of a new (2+1)- dimensional generalized KdV equation
Lower bounds for the Hilbert number of polynomial systems
Exstence of exact families of travelling wave solutions for the sixth-order Ramani equation and coup
Darboux polynomials and rational first integrals of the generalized Lorenz systems
Dominated splittings and Pesin formula
Deviation property of periodic measures in C1 nonuniformly hyperbolic systems with limit domination
两非线性波方程真圈解的存在性和破缺性质
Existence and breaking property of real loop-solutions of two nonlinear wave equations
The Travelling Wave Solutions for （2＋1）-dimensional AKNS Equation
弱化希尔伯特第16问题及其研究现状
Binary Bell polynomial application in generalized （2＋1）-dimensional KdV equation with variable coefficients
Riemann theta function periodic wave solutions for the variable-coefficient mKdV equation
EXACT DARK SOLITON AND ITS PERSISTENCE IN THE PERTURBED （2＋1）-DIMENSIONAL DAVEY-STEWARTSON SYSTEM
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