Synchronization and intermittency of the two point motion.

在涉及粒子或状态随时间变化的动态系统的研究中，对“两点运动”的研究是一个基本的问题。这种现象的重点是理解同一系统中两个粒子随时间的演变。例如，考虑种群建模的场景，其中观察两个大小相等的不同种群，以辨别它们是否收敛到共享随机状态（同步）或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间歇性的迷人现象。这需要一种特殊的行为，即两个点在很长一段时间内靠得很近，只是不可避免地再次偏离，不管它们最初是多么接近。两点运动中间歇性的复杂性仍然难以捉摸，这构成了我们理解上的一个空白。本研究项目旨在通过确定间歇性普遍存在的系统的特定类别来解决这一差距。通过全面的调查，目的是阐明产生这种有趣行为的潜在动力学，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统计与应用概率和非线性系统研究领域。

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.