Dynamic self-loops in networks of passive and active binary elements

arXiv (Cornell University)

Abstract

Models of coupled binary elements capture memory effects in complex dissipative materials, such as transient responses or sequential computing, when their interactions are chosen appropriately. However, for random interactions, self-loops - cyclic transition sequences incompatible with dissipative dynamics - dominate the response and undermine statistical approaches. Here we reveal that self-loops originate from energy injection and limit cycles in the underlying physical system. We furthermore introduce interaction ensembles that strongly suppress or completely eliminate self-loops, allowing statistical studies of memory in large dissipative systems. Our work opens a route towards a unified description of passive and active multistable materials using hysteron models.

Authors 3

1. Paul Baconnier

   Institute for Atomic and Molecular Physics

   Affiliation as printed

   AMOLF , 1098 XG Amsterdam , The Netherlands

2. Margot H. Teunisse Aachen Huygens-Kamerlingh Onnes Laboratory

   Leiden University · Institute for Atomic and Molecular Physics · Huygens Institute for History and Culture of the Netherlands

   Affiliation as printed

   AMOLF , 1098 XG Amsterdam , The Netherlands

   Huygens-Kamerlingh Onnes Laboratory , Leiden University , 2300 RA Leiden , The Netherlands

3. Martin van Hecke Aachen Huygens-Kamerlingh Onnes Laboratory

   Leiden University · Institute for Atomic and Molecular Physics · Huygens Institute for History and Culture of the Netherlands

   Affiliation as printed

   AMOLF , 1098 XG Amsterdam , The Netherlands

   Huygens-Kamerlingh Onnes Laboratory , Leiden University , 2300 RA Leiden , The Netherlands