一种新的长时滞系统时空描述：支配动力学
A new spatio-temporal description of long-delayed systems: ruling the dynamics
摘要：
由长延迟动力系统产生的数据可以通过所谓的时空表示以模式进行组织，揭示多个时间尺度作为独立自由度的作用。然而，它们作为等价的空间和时间变量的识别并不导致正确的动力学规则。我们引入了一个新的框架，在热力学极限的动力学的适当描述，提供了一个一般的途径治疗长延迟系统的偏微分方程。这种方案是通用的，并不依赖于附近的超临界分岔所需的在以前的方法。我们讨论了这种方法的一般有效性和局限性，并考虑了长延迟的可激发系统，朗道系统的典型情况。
英文摘要：
The data generated by long-delayed dynamical systems can be organized in patterns by means of the so-called spatio-temporal representation, uncovering the role of multiple time-scales as independent degrees of freedom. However, their identification as equivalent space and time variables does not lead to a correct dynamical rule. We introduce a new framework for a proper description of the dynamics in the thermodynamic limit, providing a general avenue for the treatment of long-delayed systems in terms of partial differential equations. Such scheme is generic and does not depend on the vicinity of a super-critical bifurcation as required in previous approaches. We discuss the general validity and limit of this method and consider the exemplary cases of long-delayed excitable, bistable and Landau systems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
