Dynamic Self-Loops in Networks of Passive and Active Binary Elements

Physical Review Letters, vol. 135, pp. 207402

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 Letter opens a route toward 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

   AMOLF, 1098 XG Amsterdam, The Netherlands

2. Margot Teunisse Aachen Huygens-Kamerlingh Onnes Laboratory

   Leiden University · Institute for Atomic and Molecular Physics

   Affiliation as printed

   AMOLF

   Leiden University

   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

   Affiliation as printed

   AMOLF

   Leiden University

   AMOLF, 1098 XG Amsterdam, The Netherlands

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