Analysis of almost periodic attractors for nonlinear evolution equations

非线性演化方程的近周期吸引子分析

基本信息

  • 批准号:
    08640221
  • 负责人:
  • 金额:
    $ 1.41万
  • 依托单位:
  • 依托单位国家:
    日本
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
  • 财政年份:
    1996
  • 资助国家:
    日本
  • 起止时间:
    1996 至 1997
  • 项目状态:
    已结题

项目摘要

In recent years great efforts have been made to analyze complexity or chaotic behaviors in the study of population dynamics or reaction-diffusion models. In this research we investigate almost periodic attractors for the semilinear partial differential equations by estimating their fractal dimensions. Especially, in [1] and [2] (of 11.REF.) we study a reaction-diffusion equation, assuming the periodicity of the diffusion coefficient and the nonlinear reaction function, as a model of population dynamics which has seasonal fluctuations in the diffusion rates. By using simultaneous Diophantine approximation, we can show that the dimension of the almost periodic attractor is majorized by the exponents of Holder's conditions on these periodic functions. Furthermire, in [3] we investigate a quasi-periodic solution of a linear Schrodinger equation with a quasi periodic perturbation with respect to the space variables. We can estimate the fractal dimension of the range of the solution, constructing the epsilon-almost periods, the epsilon-synchronous points in other words, by the iterative method, which depends on the simultaneous approximation for the irrational numbers of the frequencies.Calculating the dimensions of the attractors is to measure their level of complexity and randomness. On the other hand, it is well known that periodic or almost periodic states occupy the important positions as main gateways in various routes to chaos. In the following papers (of 11.REF.) by the head and co-investigators we have shown various fundamental results, which will play important and essential roles for investigating chaotic behaviors of nonlinear dynamical models.
近年来,在种群动力学或反应扩散模型的研究中,人们对复杂性或混沌行为进行了大量的研究。在本研究中,我们通过估计半线性偏微分方程概周期吸引子的分维来研究其概周期吸引子。特别是文献[1]和[2](11.REF.)在假定扩散系数和非线性反应函数具有周期性的情况下,我们研究了一类扩散率具有季节性波动的种群动力学模型。利用同时丢番图逼近,我们可以证明概周期吸引子的维度是由这些周期函数的Holder条件的指数决定的。此外,在文[3]中,我们研究了关于空间变量具有拟周期摄动的线性薛定谔方程的拟周期解。我们可以通过迭代的方法来估计解的范围的分维,即构造概数周期,也就是同步点,这依赖于对无理频率数的同时逼近。计算吸引子的维度是衡量它们的复杂性和随机性的程度。另一方面,众所周知,周期或概周期态在各种通向混沌的途径中占据着重要的地位,是通往混沌的主要通道。在下文(参考文献11.REF.)这些结果将对研究非线性动力学模型的混沌行为起到重要而重要的作用。

项目成果

期刊论文数量(42)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Koichiro Naito ;: "Dimensions of almost periodic trajectories for nonlinear evolution equations" Yokohama Math.J. 44. 93-113 (1997)
Koichiro Naito ;:“非线性演化方程的几乎周期轨迹的维数” Yokohama Math.J.
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Koichiro Naito ;: "Fractal dimensions of almost periodic attractors" Erg.Th.Dyn.Sys.16. 791-803 (1996)
Koichiro Naito ;:“几乎周期性吸引子的分形维数”Erg.Th.Dyn.Sys.16。
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Naito,Koichiro: "Dimensions of almost periodic trajectories for nonlinear evolution equations" Yokohama Math.J.に掲載予定.
内藤光一郎:“非线性演化方程的几乎周期轨迹的维数” 预定在 Yokohama Math.J 发表。
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Yokoyama,Takahisa: "Extended growth curve models with random-effect covariance structures" Commun.Statist.-Theory Meth.25・3. 571-584 (1996)
横山隆久:“具有随机效应协方差结构的扩展增长曲线模型”Commun.Statist.-Theory Meth.25・3(1996)。
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    0
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  • 通讯作者:
Koichiro Naito: "Dimensions of almost periodic trajectories for nonlinear evolution equations," Yokohama Mathematical Journal. 44. 93-113 (1997)
Koichiro Naito:“非线性演化方程的几乎周期轨迹的维数”,横滨数学杂志。
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NAITO Koichiro其他文献

NAITO Koichiro的其他文献

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{{ truncateString('NAITO Koichiro', 18)}}的其他基金

Complexity structure analysis on the orbits of solutions of nonlinear partial differential equations by p-adic analysis
基于p-adic分析的非线性偏微分方程解轨道的复杂结构分析
  • 批准号:
    24540180
  • 财政年份:
    2012
  • 资助金额:
    $ 1.41万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Complexity analysis on orbits of solutions of nonlinear partial differential equations
非线性偏微分方程解轨道的复杂性分析
  • 批准号:
    21540191
  • 财政年份:
    2009
  • 资助金额:
    $ 1.41万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Analysis on the fractal structure of complexity solutions for nonlinear differential equations
非线性微分方程复杂解的分形结构分析
  • 批准号:
    18540187
  • 财政年份:
    2006
  • 资助金额:
    $ 1.41万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Analysis on the fractal structure of quasi periodic orbits for nonlinear evolution equations
非线性演化方程准周期轨道的分形结构分析
  • 批准号:
    16540164
  • 财政年份:
    2004
  • 资助金额:
    $ 1.41万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Analysis on the structure of quasi periodic attractors for nonlinear partial differential equations
非线性偏微分方程拟周期吸引子结构分析
  • 批准号:
    14540182
  • 财政年份:
    2002
  • 资助金额:
    $ 1.41万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Analysis of dimensional and recursive properties for almost periodic solutions of nonlinear partial differential equations
非线性偏微分方程几乎周期解的维数和递归性质分析
  • 批准号:
    10640178
  • 财政年份:
    1998
  • 资助金额:
    $ 1.41万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)

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  • 批准号:
    8822565
  • 财政年份:
    1989
  • 资助金额:
    $ 1.41万
  • 项目类别:
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Mathematical Sciences: Julia Sets, Orthogonal Polynomials, And Almost-Periodicity
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  • 批准号:
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  • 财政年份:
    1984
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  • 项目类别:
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Mathematical Sciences: Julia Sets, Orthogonal Polynomials, and Almost-Periodicity
数学科学:Julia 集、正交多项式和几乎周期性
  • 批准号:
    8401921
  • 财政年份:
    1984
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