Synchronization and intermittency of the two point motion.

两点运动的同步性和间歇性。

• 批准号: 2751231
• 金额: --
• 依托单位: Imperial College London
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2022
• 资助国家: 英国
• 起止时间: 2022 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2751231
• 关键词: Synchronization; intermittency; two; point; motion.

In the study of dynamic systems involving particles or states over time, a fundamental inquiry emerges in the examination of the "two-point motion". This phenomenon focuses on understanding the evolution of two particles within the same system over time.Consider, for instance, the scenario of population modeling, where two distinct populations of equal size are observed to discern whether they converge to a shared random state (synchronization) or exhibit divergence indicative of chaotic behavior. Alternatively, a fascinating phenomenon known as intermittency in the two-point motion can occur. This entails a peculiar behavior wherein two points spend extended periods in close proximity, only to inevitably diverge again, regardless of their initial closeness.The intricacies of intermittency in the two-point motion remain elusive, constituting a gap in our understanding. This research project seeks to address this gap by identifying specific classes of systems in which intermittency is prevalent. Through comprehensive investigation, the aim is to shed light on the underlying dynamics that give rise to this intriguing behavior and contribute to a deeper comprehension of complex systems and their temporal evolution.This project falls within the EPSRC statistics and applied probability, and non-linear systems research areas.

在研究涉及粒子或状态随时间变化的动力学系统时，对“两点运动”的考察是一个基本的探索。这一现象的重点在于理解同一系统中两个粒子随时间的演化。例如，考虑种群建模的场景，观察两个相同大小的不同种群，以辨别它们是收敛到一个共享的随机状态（同步）还是表现出指示混沌行为的发散。或者，在两点运动中会出现一种被称为不稳定性的迷人现象。这就产生了一种特殊的行为，即两个点在很长一段时间内非常接近，但无论它们最初多么接近，都不可避免地再次发散。两点运动中的不连续性的复杂性仍然难以理解，这构成了我们理解的一个空白。该研究项目旨在通过确定特定类别的系统，其中不稳定性是普遍的，以解决这一差距。通过全面的调查，目的是阐明潜在的动力学，引起了这一有趣的行为，并有助于更深入地理解复杂系统及其时间演化。该项目属于EPSRC统计和应用概率，以及非线性系统的研究领域福尔斯。