论文标题
自我切换马尔可夫链：新兴的主导现象
Self-Switching Markov Chains: emerging dominance phenomena
论文作者
论文摘要
在自然界中许多动态系统中，动力学定律随系统的时间演变而变化。这些变化通常与某些事件的发生有关。这些事件发生的时机反过来取决于动态系统本身的轨迹，使系统的动力学和动力学变化的时机强烈耦合。自然，满足事件的轨迹将持续更长的时间。因此，我们期望更频繁地观察到主要动态，从长远来看，这种动态需要更长的时间。本文提出了一个称为自切换马尔可夫链（SSMC）的马尔可夫链模型，其中可以严格解决主导动态的出现。我们在SSMC中介绍条件和缩放，在该条件下，我们只有概率仅是主要动力学的子集，并且我们表征了这些主要动力学。此外，我们表明动力学之间的切换表现出类似于电竞争的特性。
In many dynamical systems in nature, the law of the dynamics changes along with the temporal evolution of the system. These changes are often associated with the occurrence of certain events. The timing of occurrence of these events depends, in turn, on the trajectory of the dynamical system itself, making the dynamics of the system and the timing of a change in the dynamics strongly coupled. Naturally, trajectories that take longer to satisfy the event will last longer. Therefore, we expect to observe more frequently the dominant dynamics, the ones that take longer to change in the long run. This article proposes a Markov chain model, called Self-Switching Markov Chain (SSMC), in which the emergence of dominant dynamics can be rigorously addressed. We present conditions and scaling in the SSMC under which we observe with probability one only the subset of dominant dynamics, and we characterize these dominant dynamics. Furthermore, we show that the switching between dynamics exhibits metastability-like property.
