| 吴玮.耦合动力系统解的延拓性[J].数学年刊A辑,2009,30(4):439~446 |
| 耦合动力系统解的延拓性 |
| Continuation of Solutions of Coupled Dynamical Systems |
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| DOI： |
| 中文关键词: 耦合动力系统 同步 存在性 唯-性 延拓性 |
| 英文关键词:Coupled dynamical systems, Synchronization, Existence, Uniqueness,
Continuation |
| 基金项目:国家自然科学基金，上海市科委(No.09DZ2272900)资助的项目 |
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| 中文摘要: |
| 近年来,人们对耦合动力系统的同步行为进行了大量的研究.在数学上,同步可以定义为:在耦合或者外力的作用下,两个或多个动力系统的行为随着时间趋于无穷而趋于一种共同状态的过程.因此,在讨论同步行为之前,必须首先解决一个关于解的延拓性的问题:对于给定的初始值,耦合系统的解是否可以延拓到正无穷,即解足否可以在无穷区间[0,+∞)上存在?提出了一个一般的耦合动力系统模型,并且证明了在QUAD假设下,该一般模型的解在区间[0,+∞)上存在. |
| 英文摘要: |
| Recently, the synchronization of coupled dynamical systems has been widely
studied. Synchronization is referred to as a process wherein two (or many) dynamical
systems are adjusted to a common behavior as time goes to infinity, due to coupling or
forcing. Therefore, before discussing synchronization, a basic problem on continuation of the
solution must be solved: For given initial conditions, can the solution of coupled dynamical
systems be extended to the infinite interval [0,+∞)? This paper proposes a general model
of coupled dynamical systems, which includes previously studied systems as special cases,
and proves that under the assumption of QUAD (quadratic), the solution of the general
model exists on [0,+∞). |
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