Stable Synchronous Propagation of Signals by Feedforward Networks

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-01-16 DOI:10.1137/23m1552267

Ian Stewart, David Wood

引用次数: 0

Abstract

SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 167-204, March 2024.
Abstract.We analyze the dynamics of networks in which a central pattern generator (CPG) transmits signals along one or more feedforward chains in a synchronous or phase-synchronous manner. Such propagating signals are common in biology, especially in locomotion and peristalsis, and are of interest for continuum robots. We construct such networks as feedforward lifts of the CPG. If the CPG dynamics is periodic, so is the lifted dynamics. Synchrony with the CPG manifests as a standing wave, and a regular phase pattern creates a traveling wave. We discuss Liapunov, asymptotic, and Floquet stability of the lifted periodic orbit and introduce transverse versions of these conditions that imply stability for signals propagating along arbitrarily long chains. We compare these notions to a simpler condition, transverse stability of the synchrony subspace, which is equivalent to Floquet stability when nodes are 1 dimensional.

查看原文本刊更多论文

前馈网络信号的稳定同步传播

SIAM 应用动力系统期刊》，第 23 卷第 1 期，第 167-204 页，2024 年 3 月。摘要：我们分析了中央模式发生器（CPG）以同步或相位同步方式沿一条或多条前馈链传递信号的网络动力学。这种传播信号在生物学中很常见，尤其是在运动和蠕动中，对于连续机器人也很有意义。我们将这种网络构建为 CPG 的前馈提升网络。如果 CPG 的动态是周期性的，那么提升后的动态也是周期性的。与 CPG 的同步表现为驻波，而有规律的相位模式则会产生行波。我们讨论了提升周期轨道的李亚普诺夫稳定性、渐近稳定性和弗洛克特稳定性，并介绍了这些条件的横向版本，它们意味着沿任意长链传播的信号的稳定性。我们将这些概念与一个更简单的条件--同步子空间的横向稳定性--进行了比较，当节点为一维时，同步子空间的横向稳定性等同于 Floquet 稳定性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.